12x^2=9200-800x

Solution for 12x^2=9200-800x equation:

12x^2=9200-800x

We move all terms to the left:

12x^2-(9200-800x)=0

We add all the numbers together, and all the variables

12x^2-(-800x+9200)=0

We get rid of parentheses

12x^2+800x-9200=0

a = 12; b = 800; c = -9200;
Δ = b2-4ac
Δ = 8002-4·12·(-9200)
Δ = 1081600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1081600}=1040$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(800)-1040}{2*12}=\frac{-1840}{24}
=-76+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(800)+1040}{2*12}=\frac{240}{24}
=10
$