130x=2,000+40x+x2

Solution for 130x=2,000+40x+x2 equation:

130x=2.000+40x+x2

We move all terms to the left:

130x-(2.000+40x+x2)=0

We add all the numbers together, and all the variables

-(+40x+x^2+2.000)+130x=0

We get rid of parentheses

-x^2-40x+130x-2.000=0

We add all the numbers together, and all the variables

-1x^2+90x-2=0

a = -1; b = 90; c = -2;
Δ = b2-4ac
Δ = 902-4·(-1)·(-2)
Δ = 8092
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:

$\sqrt{\Delta}=\sqrt{8092}=\sqrt{1156*7}=\sqrt{1156}*\sqrt{7}=34\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-34\sqrt{7}}{2*-1}=\frac{-90-34\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+34\sqrt{7}}{2*-1}=\frac{-90+34\sqrt{7}}{-2}
$