4x2+5=-9x

Solution for 4x2+5=-9x equation:

4x^2+5=-9x

We move all terms to the left:

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

We get rid of parentheses

4x^2+9x+5=0

a = 4; b = 9; c = +5;
Δ = b2-4ac
Δ = 92-4·4·5
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-1}{2*4}=\frac{-10}{8}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+1}{2*4}=\frac{-8}{8}
=-1
$