9x^2-7=36x

Solution for 9x^2-7=36x equation:

9x^2-7=36x

We move all terms to the left:

9x^2-7-(36x)=0

a = 9; b = -36; c = -7;
Δ = b2-4ac
Δ = -362-4·9·(-7)
Δ = 1548
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:

$\sqrt{\Delta}=\sqrt{1548}=\sqrt{36*43}=\sqrt{36}*\sqrt{43}=6\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{43}}{2*9}=\frac{36-6\sqrt{43}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{43}}{2*9}=\frac{36+6\sqrt{43}}{18}
$