5+9x+4x^2=4

Solution for 5+9x+4x^2=4 equation:

5+9x+4x^2=4

We move all terms to the left:

5+9x+4x^2-(4)=0

We add all the numbers together, and all the variables

4x^2+9x+1=0

a = 4; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·4·1
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{65}}{2*4}=\frac{-9-\sqrt{65}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{65}}{2*4}=\frac{-9+\sqrt{65}}{8}
$