4x^2+24=-22x

Solution for 4x^2+24=-22x equation:

4x^2+24=-22x

We move all terms to the left:

4x^2+24-(-22x)=0

We get rid of parentheses

4x^2+22x+24=0

a = 4; b = 22; c = +24;
Δ = b2-4ac
Δ = 222-4·4·24
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-10}{2*4}=\frac{-32}{8}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+10}{2*4}=\frac{-12}{8}
=-1+1/2
$