4q^2+5q=6

Solution for 4q^2+5q=6 equation:

4q^2+5q=6

We move all terms to the left:

4q^2+5q-(6)=0

a = 4; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·4·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*4}=\frac{-16}{8}
=-2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*4}=\frac{6}{8}
=3/4
$