1.500=(800-100x)x

Solution for 1.500=(800-100x)x equation:

1.500=(800-100x)x

We move all terms to the left:

1.500-((800-100x)x)=0

We add all the numbers together, and all the variables

-((-100x+800)x)+1.500=0

We add all the numbers together, and all the variables

-((-100x+800)x)+1.5=0


We calculate terms in parentheses: -((-100x+800)x), so:

(-100x+800)x

We multiply parentheses

-100x^2+800x

Back to the equation:

-(-100x^2+800x)


We get rid of parentheses

100x^2-800x+1.5=0

a = 100; b = -800; c = +1.5;
Δ = b2-4ac
Δ = -8002-4·100·1.5
Δ = 639400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{639400}=\sqrt{100*6394}=\sqrt{100}*\sqrt{6394}=10\sqrt{6394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-10\sqrt{6394}}{2*100}=\frac{800-10\sqrt{6394}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+10\sqrt{6394}}{2*100}=\frac{800+10\sqrt{6394}}{200}
$