x(631.58-0.58x)+(288.9-0.222x)=1000

Solution for x(631.58-0.58x)+(288.9-0.222x)=1000 equation:

x(631.58-0.58x)+(288.9-0.222x)=1000

We move all terms to the left:

x(631.58-0.58x)+(288.9-0.222x)-(1000)=0

We add all the numbers together, and all the variables

x(-0.58x+631.58)+(-0.222x+288.9)-1000=0

We multiply parentheses

0x^2+631.58x+(-0.222x+288.9)-1000=0

We get rid of parentheses

0x^2+631.58x-0.222x+288.9-1000=0

We add all the numbers together, and all the variables

x^2+631.358x-711.1=0

a = 1; b = 631.358; c = -711.1;
Δ = b2-4ac
Δ = 631.3582-4·1·(-711.1)
Δ = 401457.324164
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{-(631.358)-\sqrt{401457.324164}}{2*1}=\frac{-631.358-\sqrt{401457.324164}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(631.358)+\sqrt{401457.324164}}{2*1}=\frac{-631.358+\sqrt{401457.324164}}{2}
$