25(x-3)=-8x^2

Solution for 25(x-3)=-8x^2 equation:

25(x-3)=-8x^2

We move all terms to the left:

25(x-3)-(-8x^2)=0

We multiply parentheses

-(-8x^2)+25x-75=0

We get rid of parentheses

8x^2+25x-75=0

a = 8; b = 25; c = -75;
Δ = b2-4ac
Δ = 252-4·8·(-75)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-55}{2*8}=\frac{-80}{16}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+55}{2*8}=\frac{30}{16}
=1+7/8
$