x^2+6x=x+50x2+6x=x+50

Solution for x^2+6x=x+50x2+6x=x+50 equation:

x^2+6x=x+50x^2+6x=x+50

We move all terms to the left:

x^2+6x-(x+50x^2+6x)=0

We get rid of parentheses

x^2-50x^2-x-6x+6x=0

We add all the numbers together, and all the variables

-49x^2-1x=0

a = -49; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-49)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-49}=\frac{0}{-98}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-49}=\frac{2}{-98}
=-1/49
$