2x^2-12x=162

Solution for 2x^2-12x=162 equation:

2x^2-12x=162

We move all terms to the left:

2x^2-12x-(162)=0

a = 2; b = -12; c = -162;
Δ = b2-4ac
Δ = -122-4·2·(-162)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{10}}{2*2}=\frac{12-12\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{10}}{2*2}=\frac{12+12\sqrt{10}}{4}
$