15a^2-4a=3

Solution for 15a^2-4a=3 equation:

15a^2-4a=3

We move all terms to the left:

15a^2-4a-(3)=0

a = 15; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·15·(-3)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-14}{2*15}=\frac{-10}{30}
=-1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+14}{2*15}=\frac{18}{30}
=3/5
$