Question
Find the roots
x1=43−321,x2=43+321
Alternative Form
x1≈−2.686932,x2≈4.186932
Evaluate
4x2−6x−45
To find the roots of the expression,set the expression equal to 0
4x2−6x−45=0
Substitute a=4,b=−6 and c=−45 into the quadratic formula x=2a−b±b2−4ac
x=2×46±(−6)2−4×4(−45)
Simplify the expression
x=86±(−6)2−4×4(−45)
Simplify the expression
More Steps

Evaluate
(−6)2−4×4(−45)
Multiply
More Steps

Multiply the terms
4×4(−45)
Rewrite the expression
−4×4×45
Multiply the terms
−720
(−6)2−(−720)
Rewrite the expression
62−(−720)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
62+720
Evaluate the power
36+720
Add the numbers
756
x=86±756
Simplify the radical expression
More Steps

Evaluate
756
Write the expression as a product where the root of one of the factors can be evaluated
36×21
Write the number in exponential form with the base of 6
62×21
The root of a product is equal to the product of the roots of each factor
62×21
Reduce the index of the radical and exponent with 2
621
x=86±621
Separate the equation into 2 possible cases
x=86+621x=86−621
Simplify the expression
More Steps

Evaluate
x=86+621
Divide the terms
More Steps

Evaluate
86+621
Rewrite the expression
82(3+321)
Cancel out the common factor 2
43+321
x=43+321
x=43+321x=86−621
Simplify the expression
More Steps

Evaluate
x=86−621
Divide the terms
More Steps

Evaluate
86−621
Rewrite the expression
82(3−321)
Cancel out the common factor 2
43−321
x=43−321
x=43+321x=43−321
Solution
x1=43−321,x2=43+321
Alternative Form
x1≈−2.686932,x2≈4.186932
Show Solution
