40-6q+0.25q^2=35-7q+0.5q^2

Solution for 40-6q+0.25q^2=35-7q+0.5q^2 equation:

40-6q+0.25q^2=35-7q+0.5q^2

We move all terms to the left:

40-6q+0.25q^2-(35-7q+0.5q^2)=0

We get rid of parentheses

0.25q^2-0.5q^2+7q-6q-35+40=0

We add all the numbers together, and all the variables

-0.25q^2+q+5=0

a = -0.25; b = 1; c = +5;
Δ = b2-4ac
Δ = 12-4·(-0.25)·5
Δ = 6
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{6}}{2*-0.25}=\frac{-1-\sqrt{6}}{-0.5}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{6}}{2*-0.25}=\frac{-1+\sqrt{6}}{-0.5}
$