(-5x+32)=(-20x+48)x

Solution for (-5x+32)=(-20x+48)x equation:

(-5x+32)=(-20x+48)x

We move all terms to the left:

(-5x+32)-((-20x+48)x)=0

We get rid of parentheses

-5x-((-20x+48)x)+32=0


We calculate terms in parentheses: -((-20x+48)x), so:

(-20x+48)x

We multiply parentheses

-20x^2+48x

Back to the equation:

-(-20x^2+48x)


We get rid of parentheses

20x^2-48x-5x+32=0

We add all the numbers together, and all the variables

20x^2-53x+32=0

a = 20; b = -53; c = +32;
Δ = b2-4ac
Δ = -532-4·20·32
Δ = 249
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{-(-53)-\sqrt{249}}{2*20}=\frac{53-\sqrt{249}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{249}}{2*20}=\frac{53+\sqrt{249}}{40}
$