4(x^2)+26(x)-12=0

Solution for 4(x^2)+26(x)-12=0 equation:

4(x^2)+26(x)-12=0

a = 4; b = 26; c = -12;
Δ = b2-4ac
Δ = 262-4·4·(-12)
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{217}}{2*4}=\frac{-26-2\sqrt{217}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{217}}{2*4}=\frac{-26+2\sqrt{217}}{8}
$