Question
Find the roots
x1=31−19,x2=31+19
Alternative Form
x1≈−1.119633,x2≈1.7863
Evaluate
3x2−2x−6
To find the roots of the expression,set the expression equal to 0
3x2−2x−6=0
Substitute a=3,b=−2 and c=−6 into the quadratic formula x=2a−b±b2−4ac
x=2×32±(−2)2−4×3(−6)
Simplify the expression
x=62±(−2)2−4×3(−6)
Simplify the expression
More Steps

Evaluate
(−2)2−4×3(−6)
Multiply
More Steps

Multiply the terms
4×3(−6)
Rewrite the expression
−4×3×6
Multiply the terms
−72
(−2)2−(−72)
Rewrite the expression
22−(−72)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
22+72
Evaluate the power
4+72
Add the numbers
76
x=62±76
Simplify the radical expression
More Steps

Evaluate
76
Write the expression as a product where the root of one of the factors can be evaluated
4×19
Write the number in exponential form with the base of 2
22×19
The root of a product is equal to the product of the roots of each factor
22×19
Reduce the index of the radical and exponent with 2
219
x=62±219
Separate the equation into 2 possible cases
x=62+219x=62−219
Simplify the expression
More Steps

Evaluate
x=62+219
Divide the terms
More Steps

Evaluate
62+219
Rewrite the expression
62(1+19)
Cancel out the common factor 2
31+19
x=31+19
x=31+19x=62−219
Simplify the expression
More Steps

Evaluate
x=62−219
Divide the terms
More Steps

Evaluate
62−219
Rewrite the expression
62(1−19)
Cancel out the common factor 2
31−19
x=31−19
x=31+19x=31−19
Solution
x1=31−19,x2=31+19
Alternative Form
x1≈−1.119633,x2≈1.7863
Show Solution
