x(x+1)=2x+7

Solution for x(x+1)=2x+7 equation:

x(x+1)=2x+7

We move all terms to the left:

x(x+1)-(2x+7)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-1x-7=0

a = 1; b = -1; c = -7;
Δ = b2-4ac
Δ = -12-4·1·(-7)
Δ = 29
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{-(-1)-\sqrt{29}}{2*1}=\frac{1-\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{29}}{2*1}=\frac{1+\sqrt{29}}{2}
$