6x^2-3x+9x=4

Solution for 6x^2-3x+9x=4 equation:

6x^2-3x+9x=4

We move all terms to the left:

6x^2-3x+9x-(4)=0

We add all the numbers together, and all the variables

6x^2+6x-4=0

a = 6; b = 6; c = -4;
Δ = b2-4ac
Δ = 62-4·6·(-4)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{33}}{2*6}=\frac{-6-2\sqrt{33}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{33}}{2*6}=\frac{-6+2\sqrt{33}}{12}
$