6x^2=6+9x

Solution for 6x^2=6+9x equation:

6x^2=6+9x

We move all terms to the left:

6x^2-(6+9x)=0

We add all the numbers together, and all the variables

6x^2-(9x+6)=0

We get rid of parentheses

6x^2-9x-6=0

a = 6; b = -9; c = -6;
Δ = b2-4ac
Δ = -92-4·6·(-6)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*6}=\frac{-6}{12}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*6}=\frac{24}{12}
=2
$