6x^2+26x-26=0

Solution for 6x^2+26x-26=0 equation:

6x^2+26x-26=0

a = 6; b = 26; c = -26;
Δ = b2-4ac
Δ = 262-4·6·(-26)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-10\sqrt{13}}{2*6}=\frac{-26-10\sqrt{13}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+10\sqrt{13}}{2*6}=\frac{-26+10\sqrt{13}}{12}
$