8x-3x=(8-x)x

Solution for 8x-3x=(8-x)x equation:

8x-3x=(8-x)x

We move all terms to the left:

8x-3x-((8-x)x)=0

We add all the numbers together, and all the variables

8x-3x-((-1x+8)x)=0

We add all the numbers together, and all the variables

5x-((-1x+8)x)=0


We calculate terms in parentheses: -((-1x+8)x), so:

(-1x+8)x

We multiply parentheses

-1x^2+8x

Back to the equation:

-(-1x^2+8x)


We get rid of parentheses

1x^2-8x+5x=0

We add all the numbers together, and all the variables

x^2-3x=0

a = 1; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·1·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*1}=\frac{6}{2}
=3
$