x*(x+7)=(x+3)

Solution for x*(x+7)=(x+3) equation:

x(x+7)=(x+3)

We move all terms to the left:

x(x+7)-((x+3))=0

We multiply parentheses

x^2+7x-((x+3))=0


We calculate terms in parentheses: -((x+3)), so:

(x+3)

We get rid of parentheses

x+3

Back to the equation:

-(x+3)


We get rid of parentheses

x^2+7x-x-3=0

We add all the numbers together, and all the variables

x^2+6x-3=0

a = 1; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·1·(-3)
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{3}}{2*1}=\frac{-6-4\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{3}}{2*1}=\frac{-6+4\sqrt{3}}{2}
$