800=1.5x^2-(20+5x)

Solution for 800=1.5x^2-(20+5x) equation:

800=1.5x^2-(20+5x)

We move all terms to the left:

800-(1.5x^2-(20+5x))=0

We add all the numbers together, and all the variables

-(1.5x^2-(5x+20))+800=0


We calculate terms in parentheses: -(1.5x^2-(5x+20)), so:

1.5x^2-(5x+20)

We get rid of parentheses

1.5x^2-5x-20

Back to the equation:

-(1.5x^2-5x-20)


We get rid of parentheses

-1.5x^2+5x+20+800=0

We add all the numbers together, and all the variables

-1.5x^2+5x+820=0

a = -1.5; b = 5; c = +820;
Δ = b2-4ac
Δ = 52-4·(-1.5)·820
Δ = 4945
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{-(5)-\sqrt{4945}}{2*-1.5}=\frac{-5-\sqrt{4945}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{4945}}{2*-1.5}=\frac{-5+\sqrt{4945}}{-3}
$