x^2-5x=142

Solution for x^2-5x=142 equation:

x^2-5x=142

We move all terms to the left:

x^2-5x-(142)=0

a = 1; b = -5; c = -142;
Δ = b2-4ac
Δ = -52-4·1·(-142)
Δ = 593
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{-(-5)-\sqrt{593}}{2*1}=\frac{5-\sqrt{593}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{593}}{2*1}=\frac{5+\sqrt{593}}{2}
$