5=9x^2-4x-15

Solution for 5=9x^2-4x-15 equation:

5=9x^2-4x-15

We move all terms to the left:

5-(9x^2-4x-15)=0

We get rid of parentheses

-9x^2+4x+15+5=0

We add all the numbers together, and all the variables

-9x^2+4x+20=0

a = -9; b = 4; c = +20;
Δ = b2-4ac
Δ = 42-4·(-9)·20
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{46}}{2*-9}=\frac{-4-4\sqrt{46}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{46}}{2*-9}=\frac{-4+4\sqrt{46}}{-18}
$