X(2x-15)=27

Solution for X(2x-15)=27 equation:

X(2X-15)=27

We move all terms to the left:

X(2X-15)-(27)=0

We multiply parentheses

2X^2-15X-27=0

a = 2; b = -15; c = -27;
Δ = b2-4ac
Δ = -152-4·2·(-27)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-21}{2*2}=\frac{-6}{4}
=-1+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+21}{2*2}=\frac{36}{4}
=9
$