4x2+8x-13=32-23x

Solution for 4x2+8x-13=32-23x equation:

4x^2+8x-13=32-23x

We move all terms to the left:

4x^2+8x-13-(32-23x)=0

We add all the numbers together, and all the variables

4x^2+8x-(-23x+32)-13=0

We get rid of parentheses

4x^2+8x+23x-32-13=0

We add all the numbers together, and all the variables

4x^2+31x-45=0

a = 4; b = 31; c = -45;
Δ = b2-4ac
Δ = 312-4·4·(-45)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-41}{2*4}=\frac{-72}{8}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+41}{2*4}=\frac{10}{8}
=1+1/4
$