4q^2=11q-2

Solution for 4q^2=11q-2 equation:

4q^2=11q-2

We move all terms to the left:

4q^2-(11q-2)=0

We get rid of parentheses

4q^2-11q+2=0

a = 4; b = -11; c = +2;
Δ = b2-4ac
Δ = -112-4·4·2
Δ = 89
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{-(-11)-\sqrt{89}}{2*4}=\frac{11-\sqrt{89}}{8}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{89}}{2*4}=\frac{11+\sqrt{89}}{8}
$