23x^2-75x-20=0

Solution for 23x^2-75x-20=0 equation:

23x^2-75x-20=0

a = 23; b = -75; c = -20;
Δ = b2-4ac
Δ = -752-4·23·(-20)
Δ = 7465
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{-(-75)-\sqrt{7465}}{2*23}=\frac{75-\sqrt{7465}}{46}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{7465}}{2*23}=\frac{75+\sqrt{7465}}{46}
$