0=9x^2+6x-74

Solution for 0=9x^2+6x-74 equation:

0=9x^2+6x-74

We move all terms to the left:

0-(9x^2+6x-74)=0

We add all the numbers together, and all the variables

-(9x^2+6x-74)=0

We get rid of parentheses

-9x^2-6x+74=0

a = -9; b = -6; c = +74;
Δ = b2-4ac
Δ = -62-4·(-9)·74
Δ = 2700
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:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-30\sqrt{3}}{2*-9}=\frac{6-30\sqrt{3}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30\sqrt{3}}{2*-9}=\frac{6+30\sqrt{3}}{-18}
$