(X-6)2x=90

Solution for (X-6)2x=90 equation:

(X-6)2X=90

We move all terms to the left:

(X-6)2X-(90)=0

We multiply parentheses

2X^2-12X-90=0

a = 2; b = -12; c = -90;
Δ = b2-4ac
Δ = -122-4·2·(-90)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{6}}{2*2}=\frac{12-12\sqrt{6}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{6}}{2*2}=\frac{12+12\sqrt{6}}{4}
$