61x^2-20x-32=0

Solution for 61x^2-20x-32=0 equation:

61x^2-20x-32=0

a = 61; b = -20; c = -32;
Δ = b2-4ac
Δ = -202-4·61·(-32)
Δ = 8208
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:

$\sqrt{\Delta}=\sqrt{8208}=\sqrt{144*57}=\sqrt{144}*\sqrt{57}=12\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-12\sqrt{57}}{2*61}=\frac{20-12\sqrt{57}}{122}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+12\sqrt{57}}{2*61}=\frac{20+12\sqrt{57}}{122}
$