5x-8=20x2-32x

Solution for 5x-8=20x2-32x equation:

5x-8=20x^2-32x

We move all terms to the left:

5x-8-(20x^2-32x)=0

We get rid of parentheses

-20x^2+5x+32x-8=0

We add all the numbers together, and all the variables

-20x^2+37x-8=0

a = -20; b = 37; c = -8;
Δ = b2-4ac
Δ = 372-4·(-20)·(-8)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-27}{2*-20}=\frac{-64}{-40}
=1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+27}{2*-20}=\frac{-10}{-40}
=1/4
$