4a^2=4a+15

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

4a^2=4a+15

We move all terms to the left:

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

We get rid of parentheses

4a^2-4a-15=0

a = 4; b = -4; c = -15;
Δ = b2-4ac
Δ = -42-4·4·(-15)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16}{2*4}=\frac{-12}{8}
=-1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*4}=\frac{20}{8}
=2+1/2
$