24x^2=-64+80x

Solution for 24x^2=-64+80x equation:

24x^2=-64+80x

We move all terms to the left:

24x^2-(-64+80x)=0

We add all the numbers together, and all the variables

24x^2-(80x-64)=0

We get rid of parentheses

24x^2-80x+64=0

a = 24; b = -80; c = +64;
Δ = b2-4ac
Δ = -802-4·24·64
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-16}{2*24}=\frac{64}{48}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+16}{2*24}=\frac{96}{48}
=2
$