5a2+4a=5

Solution for 5a2+4a=5 equation:

5a^2+4a=5

We move all terms to the left:

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

a = 5; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·5·(-5)
Δ = 116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{29}}{2*5}=\frac{-4-2\sqrt{29}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{29}}{2*5}=\frac{-4+2\sqrt{29}}{10}
$