6x^2+12x-17=0

Solution for 6x^2+12x-17=0 equation:

6x^2+12x-17=0

a = 6; b = 12; c = -17;
Δ = b2-4ac
Δ = 122-4·6·(-17)
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{138}}{2*6}=\frac{-12-2\sqrt{138}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{138}}{2*6}=\frac{-12+2\sqrt{138}}{12}
$