x(9x-22)=15

Solution for x(9x-22)=15 equation:

x(9x-22)=15

We move all terms to the left:

x(9x-22)-(15)=0

We multiply parentheses

9x^2-22x-15=0

a = 9; b = -22; c = -15;
Δ = b2-4ac
Δ = -222-4·9·(-15)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-32}{2*9}=\frac{-10}{18}
=-5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+32}{2*9}=\frac{54}{18}
=3
$