X(2x-6)=15

Solution for X(2x-6)=15 equation:

X(2X-6)=15

We move all terms to the left:

X(2X-6)-(15)=0

We multiply parentheses

2X^2-6X-15=0

a = 2; b = -6; c = -15;
Δ = b2-4ac
Δ = -62-4·2·(-15)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*2}=\frac{6-2\sqrt{39}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*2}=\frac{6+2\sqrt{39}}{4}
$