6x^2-26x-9=0

Solution for 6x^2-26x-9=0 equation:

6x^2-26x-9=0

a = 6; b = -26; c = -9;
Δ = b2-4ac
Δ = -262-4·6·(-9)
Δ = 892
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:

$\sqrt{\Delta}=\sqrt{892}=\sqrt{4*223}=\sqrt{4}*\sqrt{223}=2\sqrt{223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{223}}{2*6}=\frac{26-2\sqrt{223}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{223}}{2*6}=\frac{26+2\sqrt{223}}{12}
$