4a^2=5a+3

Solution for 4a^2=5a+3 equation:

4a^2=5a+3

We move all terms to the left:

4a^2-(5a+3)=0

We get rid of parentheses

4a^2-5a-3=0

a = 4; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·4·(-3)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{73}}{2*4}=\frac{5-\sqrt{73}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*4}=\frac{5+\sqrt{73}}{8}
$