6x^2-12x-87=4

Solution for 6x^2-12x-87=4 equation:

6x^2-12x-87=4

We move all terms to the left:

6x^2-12x-87-(4)=0

We add all the numbers together, and all the variables

6x^2-12x-91=0

a = 6; b = -12; c = -91;
Δ = b2-4ac
Δ = -122-4·6·(-91)
Δ = 2328
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:

$\sqrt{\Delta}=\sqrt{2328}=\sqrt{4*582}=\sqrt{4}*\sqrt{582}=2\sqrt{582}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{582}}{2*6}=\frac{12-2\sqrt{582}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{582}}{2*6}=\frac{12+2\sqrt{582}}{12}
$