x^2+2x=7x+27

Solution for x^2+2x=7x+27 equation:

x^2+2x=7x+27

We move all terms to the left:

x^2+2x-(7x+27)=0

We get rid of parentheses

x^2+2x-7x-27=0

We add all the numbers together, and all the variables

x^2-5x-27=0

a = 1; b = -5; c = -27;
Δ = b2-4ac
Δ = -52-4·1·(-27)
Δ = 133
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{133}}{2*1}=\frac{5-\sqrt{133}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{133}}{2*1}=\frac{5+\sqrt{133}}{2}
$