4x^2+17-32=-15x+100

Solution for 4x^2+17-32=-15x+100 equation:

4x^2+17-32=-15x+100

We move all terms to the left:

4x^2+17-32-(-15x+100)=0

We add all the numbers together, and all the variables

4x^2-(-15x+100)-15=0

We get rid of parentheses

4x^2+15x-100-15=0

We add all the numbers together, and all the variables

4x^2+15x-115=0

a = 4; b = 15; c = -115;
Δ = b2-4ac
Δ = 152-4·4·(-115)
Δ = 2065
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{-(15)-\sqrt{2065}}{2*4}=\frac{-15-\sqrt{2065}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{2065}}{2*4}=\frac{-15+\sqrt{2065}}{8}
$