4q^2-15q=4

Solution for 4q^2-15q=4 equation:

4q^2-15q=4

We move all terms to the left:

4q^2-15q-(4)=0

a = 4; b = -15; c = -4;
Δ = b2-4ac
Δ = -152-4·4·(-4)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-17}{2*4}=\frac{-2}{8}
=-1/4
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+17}{2*4}=\frac{32}{8}
=4
$