18x^2-9x=7

Solution for 18x^2-9x=7 equation:

18x^2-9x=7

We move all terms to the left:

18x^2-9x-(7)=0

a = 18; b = -9; c = -7;
Δ = b2-4ac
Δ = -92-4·18·(-7)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{65}}{2*18}=\frac{9-3\sqrt{65}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{65}}{2*18}=\frac{9+3\sqrt{65}}{36}
$