9x^2=12x+4

Solution for 9x^2=12x+4 equation:

9x^2=12x+4

We move all terms to the left:

9x^2-(12x+4)=0

We get rid of parentheses

9x^2-12x-4=0

a = 9; b = -12; c = -4;
Δ = b2-4ac
Δ = -122-4·9·(-4)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{2}}{2*9}=\frac{12-12\sqrt{2}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{2}}{2*9}=\frac{12+12\sqrt{2}}{18}
$