6x^2-24=-7x

Solution for 6x^2-24=-7x equation:

6x^2-24=-7x

We move all terms to the left:

6x^2-24-(-7x)=0

We get rid of parentheses

6x^2+7x-24=0

a = 6; b = 7; c = -24;
Δ = b2-4ac
Δ = 72-4·6·(-24)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-25}{2*6}=\frac{-32}{12}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+25}{2*6}=\frac{18}{12}
=1+1/2
$