8x^2+11x-59=0

Solution for 8x^2+11x-59=0 equation:

8x^2+11x-59=0

a = 8; b = 11; c = -59;
Δ = b2-4ac
Δ = 112-4·8·(-59)
Δ = 2009
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:

$\sqrt{\Delta}=\sqrt{2009}=\sqrt{49*41}=\sqrt{49}*\sqrt{41}=7\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-7\sqrt{41}}{2*8}=\frac{-11-7\sqrt{41}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+7\sqrt{41}}{2*8}=\frac{-11+7\sqrt{41}}{16}
$