6x^2+34x-20=0

Solution for 6x^2+34x-20=0 equation:

6x^2+34x-20=0

a = 6; b = 34; c = -20;
Δ = b2-4ac
Δ = 342-4·6·(-20)
Δ = 1636
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:

$\sqrt{\Delta}=\sqrt{1636}=\sqrt{4*409}=\sqrt{4}*\sqrt{409}=2\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{409}}{2*6}=\frac{-34-2\sqrt{409}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{409}}{2*6}=\frac{-34+2\sqrt{409}}{12}
$