24x^2+32x-44=-2x+1

Solution for 24x^2+32x-44=-2x+1 equation:

24x^2+32x-44=-2x+1

We move all terms to the left:

24x^2+32x-44-(-2x+1)=0

We get rid of parentheses

24x^2+32x+2x-1-44=0

We add all the numbers together, and all the variables

24x^2+34x-45=0

a = 24; b = 34; c = -45;
Δ = b2-4ac
Δ = 342-4·24·(-45)
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-74}{2*24}=\frac{-108}{48}
=-2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+74}{2*24}=\frac{40}{48}
=5/6
$