800=(0.638(x^2))+6.671x+627.619

Solution for 800=(0.638(x^2))+6.671x+627.619 equation:

800=(0.638(x^2))+6.671x+627.619

We move all terms to the left:

800-((0.638(x^2))+6.671x+627.619)=0


We calculate terms in parentheses: -((0.638x^2)+6.671x+627.619), so:

(0.638x^2)+6.671x+627.619

We add all the numbers together, and all the variables

6.671x+(0.638x^2)+627.619

We get rid of parentheses

0.638x^2+6.671x+627.619

Back to the equation:

-(0.638x^2+6.671x+627.619)


We get rid of parentheses

-0.638x^2-6.671x-627.619+800=0

We add all the numbers together, and all the variables

-0.638x^2-6.671x+172.381=0

a = -0.638; b = -6.671; c = +172.381;
Δ = b2-4ac
Δ = -6.6712-4·(-0.638)·172.381
Δ = 484.418553
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{-(-6.671)-\sqrt{484.418553}}{2*-0.638}=\frac{6.671-\sqrt{484.418553}}{-1.276}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.671)+\sqrt{484.418553}}{2*-0.638}=\frac{6.671+\sqrt{484.418553}}{-1.276}
$