(x-15)(4x-15)=9x

Solution for (x-15)(4x-15)=9x equation:

(x-15)(4x-15)=9x

We move all terms to the left:

(x-15)(4x-15)-(9x)=0

We add all the numbers together, and all the variables

-9x+(x-15)(4x-15)=0

We multiply parentheses ..

(+4x^2-15x-60x+225)-9x=0

We get rid of parentheses

4x^2-15x-60x-9x+225=0

We add all the numbers together, and all the variables

4x^2-84x+225=0

a = 4; b = -84; c = +225;
Δ = b2-4ac
Δ = -842-4·4·225
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-24\sqrt{6}}{2*4}=\frac{84-24\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+24\sqrt{6}}{2*4}=\frac{84+24\sqrt{6}}{8}
$