23x^2-123x+40=0

Solution for 23x^2-123x+40=0 equation:

23x^2-123x+40=0

a = 23; b = -123; c = +40;
Δ = b2-4ac
Δ = -1232-4·23·40
Δ = 11449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11449}=107$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-123)-107}{2*23}=\frac{16}{46}
=8/23
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-123)+107}{2*23}=\frac{230}{46}
=5
$