x2+11x=7x+21x2+11x=7x+2

Solution for x2+11x=7x+21x2+11x=7x+2 equation:

x2+11x=7x+21x^2+11x=7x+2

We move all terms to the left:

x2+11x-(7x+21x^2+11x)=0

We add all the numbers together, and all the variables

x^2-(7x+21x^2+11x)+11x=0

We get rid of parentheses

x^2-21x^2-7x-11x+11x=0

We add all the numbers together, and all the variables

-20x^2-7x=0

a = -20; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-20)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-20}=\frac{0}{-40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-20}=\frac{14}{-40}
=-7/20
$