-24=x(3x+22)

Solution for -24=x(3x+22) equation:

-24=x(3x+22)

We move all terms to the left:

-24-(x(3x+22))=0


We calculate terms in parentheses: -(x(3x+22)), so:

x(3x+22)

We multiply parentheses

3x^2+22x

Back to the equation:

-(3x^2+22x)


We get rid of parentheses

-3x^2-22x-24=0

a = -3; b = -22; c = -24;
Δ = b2-4ac
Δ = -222-4·(-3)·(-24)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-14}{2*-3}=\frac{8}{-6}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+14}{2*-3}=\frac{36}{-6}
=-6
$