7x-9=8x^2-20x

Solution for 7x-9=8x^2-20x equation:

7x-9=8x^2-20x

We move all terms to the left:

7x-9-(8x^2-20x)=0

We get rid of parentheses

-8x^2+7x+20x-9=0

We add all the numbers together, and all the variables

-8x^2+27x-9=0

a = -8; b = 27; c = -9;
Δ = b2-4ac
Δ = 272-4·(-8)·(-9)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-21}{2*-8}=\frac{-48}{-16}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+21}{2*-8}=\frac{-6}{-16}
=3/8
$