18=6x^2+9x-60

Solution for 18=6x^2+9x-60 equation:

18=6x^2+9x-60

We move all terms to the left:

18-(6x^2+9x-60)=0

We get rid of parentheses

-6x^2-9x+60+18=0

We add all the numbers together, and all the variables

-6x^2-9x+78=0

a = -6; b = -9; c = +78;
Δ = b2-4ac
Δ = -92-4·(-6)·78
Δ = 1953
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:

$\sqrt{\Delta}=\sqrt{1953}=\sqrt{9*217}=\sqrt{9}*\sqrt{217}=3\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{217}}{2*-6}=\frac{9-3\sqrt{217}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{217}}{2*-6}=\frac{9+3\sqrt{217}}{-12}
$