8x^2-30x+54=2x^2+30x

Solution for 8x^2-30x+54=2x^2+30x equation:

8x^2-30x+54=2x^2+30x

We move all terms to the left:

8x^2-30x+54-(2x^2+30x)=0

We get rid of parentheses

8x^2-2x^2-30x-30x+54=0

We add all the numbers together, and all the variables

6x^2-60x+54=0

a = 6; b = -60; c = +54;
Δ = b2-4ac
Δ = -602-4·6·54
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-48}{2*6}=\frac{12}{12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+48}{2*6}=\frac{108}{12}
=9
$