40x-x2=111

Solution for 40x-x2=111 equation:

40x-x2=111

We move all terms to the left:

40x-x2-(111)=0

We add all the numbers together, and all the variables

-1x^2+40x-111=0

a = -1; b = 40; c = -111;
Δ = b2-4ac
Δ = 402-4·(-1)·(-111)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-34}{2*-1}=\frac{-74}{-2}
=+37
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+34}{2*-1}=\frac{-6}{-2}
=+3
$