5x^2+17x-24=-9+7x

Solution for 5x^2+17x-24=-9+7x equation:

5x^2+17x-24=-9+7x

We move all terms to the left:

5x^2+17x-24-(-9+7x)=0

We add all the numbers together, and all the variables

5x^2+17x-(7x-9)-24=0

We get rid of parentheses

5x^2+17x-7x+9-24=0

We add all the numbers together, and all the variables

5x^2+10x-15=0

a = 5; b = 10; c = -15;
Δ = b2-4ac
Δ = 102-4·5·(-15)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-20}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+20}{2*5}=\frac{10}{10}
=1
$