3x(x+3)=x+7

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

3x(x+3)=x+7

We move all terms to the left:

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

We multiply parentheses

3x^2+9x-(x+7)=0

We get rid of parentheses

3x^2+9x-x-7=0

We add all the numbers together, and all the variables

3x^2+8x-7=0

a = 3; b = 8; c = -7;
Δ = b2-4ac
Δ = 82-4·3·(-7)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{37}}{2*3}=\frac{-8-2\sqrt{37}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{37}}{2*3}=\frac{-8+2\sqrt{37}}{6}
$