9X^2+18x=4

Solution for 9X^2+18x=4 equation:

9X^2+18X=4

We move all terms to the left:

9X^2+18X-(4)=0

a = 9; b = 18; c = -4;
Δ = b2-4ac
Δ = 182-4·9·(-4)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{13}}{2*9}=\frac{-18-6\sqrt{13}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{13}}{2*9}=\frac{-18+6\sqrt{13}}{18}
$