40=c+c2-101

Solution for 40=c+c2-101 equation:

40=c+c2-101

We move all terms to the left:

40-(c+c2-101)=0

We add all the numbers together, and all the variables

-(+c+c^2-101)+40=0

We get rid of parentheses

-c^2-c+101+40=0

We add all the numbers together, and all the variables

-1c^2-1c+141=0

a = -1; b = -1; c = +141;
Δ = b2-4ac
Δ = -12-4·(-1)·141
Δ = 565
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{565}}{2*-1}=\frac{1-\sqrt{565}}{-2}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{565}}{2*-1}=\frac{1+\sqrt{565}}{-2}
$