18x+9=2x^2+6x-6

Solution for 18x+9=2x^2+6x-6 equation:

18x+9=2x^2+6x-6

We move all terms to the left:

18x+9-(2x^2+6x-6)=0

We get rid of parentheses

-2x^2+18x-6x+6+9=0

We add all the numbers together, and all the variables

-2x^2+12x+15=0

a = -2; b = 12; c = +15;
Δ = b2-4ac
Δ = 122-4·(-2)·15
Δ = 264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{66}}{2*-2}=\frac{-12-2\sqrt{66}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{66}}{2*-2}=\frac{-12+2\sqrt{66}}{-4}
$