40x2+220x=-100

Solution for 40x2+220x=-100 equation:

40x^2+220x=-100

We move all terms to the left:

40x^2+220x-(-100)=0

We add all the numbers together, and all the variables

40x^2+220x+100=0

a = 40; b = 220; c = +100;
Δ = b2-4ac
Δ = 2202-4·40·100
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(220)-180}{2*40}=\frac{-400}{80}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(220)+180}{2*40}=\frac{-40}{80}
=-1/2
$