4a^2+15a=4

Solution for 4a^2+15a=4 equation:

4a^2+15a=4

We move all terms to the left:

4a^2+15a-(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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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