2a^2=5a+4

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

2a^2=5a+4

We move all terms to the left:

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

We get rid of parentheses

2a^2-5a-4=0

a = 2; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·2·(-4)
Δ = 57
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{57}}{2*2}=\frac{5-\sqrt{57}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{57}}{2*2}=\frac{5+\sqrt{57}}{4}
$