2x^2-12x-8=3

Solution for 2x^2-12x-8=3 equation:

2x^2-12x-8=3

We move all terms to the left:

2x^2-12x-8-(3)=0

We add all the numbers together, and all the variables

2x^2-12x-11=0

a = 2; b = -12; c = -11;
Δ = b2-4ac
Δ = -122-4·2·(-11)
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{58}}{2*2}=\frac{12-2\sqrt{58}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{58}}{2*2}=\frac{12+2\sqrt{58}}{4}
$