x2-4x=7+x

Solution for x2-4x=7+x equation:

x2-4x=7+x

We move all terms to the left:

x2-4x-(7+x)=0

We add all the numbers together, and all the variables

x2-4x-(x+7)=0

We add all the numbers together, and all the variables

x^2-4x-(x+7)=0

We get rid of parentheses

x^2-4x-x-7=0

We add all the numbers together, and all the variables

x^2-5x-7=0

a = 1; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·1·(-7)
Δ = 53
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{53}}{2*1}=\frac{5-\sqrt{53}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{53}}{2*1}=\frac{5+\sqrt{53}}{2}
$