Solve 4x^2 - 6x -45

Question

Find the roots

x_{1} = \frac{3 - 3 21}{4}, x_{2} = \frac{3 + 3 21}{4}

Alternative Form

x_{1} \approx - 2.686932, x_{2} \approx 4.186932

Evaluate

4 x^{2} - 6 x - 45

To find the roots of the expression,set the expression equal to 0

4 x^{2} - 6 x - 45 = 0

Substitute a= 4,b= - 6 and c= - 45 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 4 ( - 45 )}{2 \times 4}

Simplify the expression

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 4 ( - 45 )}{8}

Simplify the expression

More Steps

x = \frac{6 \pm 756}{8}

Simplify the radical expression

More Steps

x = \frac{6 \pm 6 21}{8}

Separate the equation into 2 possible cases

x = \frac{6 + 6 21}{8} x = \frac{6 - 6 21}{8}

Simplify the expression

More Steps

x = \frac{3 + 3 21}{4} x = \frac{6 - 6 21}{8}

Simplify the expression

More Steps

x = \frac{3 + 3 21}{4} x = \frac{3 - 3 21}{4}

Solution

x_{1} = \frac{3 - 3 21}{4}, x_{2} = \frac{3 + 3 21}{4}

Alternative Form

x_{1} \approx - 2.686932, x_{2} \approx 4.186932

Show Solution