2x^2+12x-x-4=0

Solution for 2x^2+12x-x-4=0 equation:

2x^2+12x-x-4=0

We add all the numbers together, and all the variables

2x^2+11x-4=0

a = 2; b = 11; c = -4;
Δ = b2-4ac
Δ = 112-4·2·(-4)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3\sqrt{17}}{2*2}=\frac{-11-3\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3\sqrt{17}}{2*2}=\frac{-11+3\sqrt{17}}{4}
$