4m^2-8m-59=0

Solution for 4m^2-8m-59=0 equation:

4m^2-8m-59=0

a = 4; b = -8; c = -59;
Δ = b2-4ac
Δ = -82-4·4·(-59)
Δ = 1008
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12\sqrt{7}}{2*4}=\frac{8-12\sqrt{7}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12\sqrt{7}}{2*4}=\frac{8+12\sqrt{7}}{8}
$