5x^2+17x-12=24-7x

Solution for 5x^2+17x-12=24-7x equation:

5x^2+17x-12=24-7x

We move all terms to the left:

5x^2+17x-12-(24-7x)=0

We add all the numbers together, and all the variables

5x^2+17x-(-7x+24)-12=0

We get rid of parentheses

5x^2+17x+7x-24-12=0

We add all the numbers together, and all the variables

5x^2+24x-36=0

a = 5; b = 24; c = -36;
Δ = b2-4ac
Δ = 242-4·5·(-36)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-36}{2*5}=\frac{-60}{10}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+36}{2*5}=\frac{12}{10}
=1+1/5
$