8q^2-10q=-3

Solution for 8q^2-10q=-3 equation:

8q^2-10q=-3

We move all terms to the left:

8q^2-10q-(-3)=0

We add all the numbers together, and all the variables

8q^2-10q+3=0

a = 8; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·8·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*8}=\frac{8}{16}
=1/2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*8}=\frac{12}{16}
=3/4
$