-24,91x^2+31,06x+77,55=0

Solution for -24,91x^2+31,06x+77,55=0 equation:

-24.91x^2+31.06x+77.55=0

a = -24.91; b = 31.06; c = +77.55;
Δ = b2-4ac
Δ = 31.062-4·(-24.91)·77.55
Δ = 8691.8056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31.06)-\sqrt{8691.8056}}{2*-24.91}=\frac{-31.06-\sqrt{8691.8056}}{-49.82}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31.06)+\sqrt{8691.8056}}{2*-24.91}=\frac{-31.06+\sqrt{8691.8056}}{-49.82}
$