4(x^2-14)=-25x

Solution for 4(x^2-14)=-25x equation:

4(x^2-14)=-25x

We move all terms to the left:

4(x^2-14)-(-25x)=0

We multiply parentheses

4x^2-(-25x)-56=0

We get rid of parentheses

4x^2+25x-56=0

a = 4; b = 25; c = -56;
Δ = b2-4ac
Δ = 252-4·4·(-56)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-39}{2*4}=\frac{-64}{8}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+39}{2*4}=\frac{14}{8}
=1+3/4
$