2q^2-40q+40=-3q+100

Solution for 2q^2-40q+40=-3q+100 equation:

2q^2-40q+40=-3q+100

We move all terms to the left:

2q^2-40q+40-(-3q+100)=0

We get rid of parentheses

2q^2-40q+3q-100+40=0

We add all the numbers together, and all the variables

2q^2-37q-60=0

a = 2; b = -37; c = -60;
Δ = b2-4ac
Δ = -372-4·2·(-60)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-43}{2*2}=\frac{-6}{4}
=-1+1/2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+43}{2*2}=\frac{80}{4}
=20
$