2a^2+9a=4

Solution for 2a^2+9a=4 equation:

2a^2+9a=4

We move all terms to the left:

2a^2+9a-(4)=0

a = 2; b = 9; c = -4;
Δ = b2-4ac
Δ = 92-4·2·(-4)
Δ = 113
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{-(9)-\sqrt{113}}{2*2}=\frac{-9-\sqrt{113}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{113}}{2*2}=\frac{-9+\sqrt{113}}{4}
$