# What are the roots if the equation 4(x^2-1)= -3x?

Mar 31, 2017

#### Answer:

x= $\frac{- 3 \pm \sqrt{73}}{8}$

#### Explanation:

$4 \cdot \left({x}^{2} - 1\right) = - 3 x$
$4 {x}^{2} - 4 = - 3 x$
$4 {x}^{2} + 3 x - 4 = 0$
Which follows the form of: $a {x}^{2} + b x + c = 0$

So you solve it using the discriminant

 Δ= b^2 - 4 * a * c
 Δ = 9 + 64 = 73
Δ > 0 so it has two different solutions

x1=  ( -b + sqrtΔ ) / (2 * a)
x1= $\frac{- 3 + \sqrt{73}}{8}$

x2=  ( -b - sqrtΔ ) / (2 * a)
x2= $\frac{- 3 - \sqrt{73}}{8}$