9x2=6x+4

Solution for 9x2=6x+4 equation:

9x^2=6x+4

We move all terms to the left:

9x^2-(6x+4)=0

We get rid of parentheses

9x^2-6x-4=0

a = 9; b = -6; c = -4;
Δ = b2-4ac
Δ = -62-4·9·(-4)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{5}}{2*9}=\frac{6-6\sqrt{5}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{5}}{2*9}=\frac{6+6\sqrt{5}}{18}
$