4x^2-61x-137=0

Solution for 4x^2-61x-137=0 equation:

4x^2-61x-137=0

a = 4; b = -61; c = -137;
Δ = b2-4ac
Δ = -612-4·4·(-137)
Δ = 5913
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:

$\sqrt{\Delta}=\sqrt{5913}=\sqrt{81*73}=\sqrt{81}*\sqrt{73}=9\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-9\sqrt{73}}{2*4}=\frac{61-9\sqrt{73}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+9\sqrt{73}}{2*4}=\frac{61+9\sqrt{73}}{8}
$