6x^2=90-12x

Solution for 6x^2=90-12x equation:

6x^2=90-12x

We move all terms to the left:

6x^2-(90-12x)=0

We add all the numbers together, and all the variables

6x^2-(-12x+90)=0

We get rid of parentheses

6x^2+12x-90=0

a = 6; b = 12; c = -90;
Δ = b2-4ac
Δ = 122-4·6·(-90)
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{-(12)-48}{2*6}=\frac{-60}{12}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+48}{2*6}=\frac{36}{12}
=3
$