8w^2-30w-59=0

Solution for 8w^2-30w-59=0 equation:

8w^2-30w-59=0

a = 8; b = -30; c = -59;
Δ = b2-4ac
Δ = -302-4·8·(-59)
Δ = 2788
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2788}=\sqrt{4*697}=\sqrt{4}*\sqrt{697}=2\sqrt{697}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{697}}{2*8}=\frac{30-2\sqrt{697}}{16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{697}}{2*8}=\frac{30+2\sqrt{697}}{16}
$