7x2-24=-x

Solution for 7x2-24=-x equation:

7x^2-24=-x

We move all terms to the left:

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

We add all the numbers together, and all the variables

7x^2-(-1x)-24=0

We get rid of parentheses

7x^2+1x-24=0

We add all the numbers together, and all the variables

7x^2+x-24=0

a = 7; b = 1; c = -24;
Δ = b2-4ac
Δ = 12-4·7·(-24)
Δ = 673
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{-(1)-\sqrt{673}}{2*7}=\frac{-1-\sqrt{673}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{673}}{2*7}=\frac{-1+\sqrt{673}}{14}
$