6x^2+x=504-x

Solution for 6x^2+x=504-x equation:

6x^2+x=504-x

We move all terms to the left:

6x^2+x-(504-x)=0

We add all the numbers together, and all the variables

6x^2+x-(-1x+504)=0

We get rid of parentheses

6x^2+x+1x-504=0

We add all the numbers together, and all the variables

6x^2+2x-504=0

a = 6; b = 2; c = -504;
Δ = b2-4ac
Δ = 22-4·6·(-504)
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-110}{2*6}=\frac{-112}{12}
=-9+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+110}{2*6}=\frac{108}{12}
=9
$