x-7=-3(x+1)/3

Solution for x-7=-3(x+1)/3 equation:

x-7=-3(x+1)/3

We move all terms to the left:

x-7-(-3(x+1)/3)=0

We multiply all the terms by the denominator


x*3)-(-3(x+1)-7*3)=0

We add all the numbers together, and all the variables

x*3)-(-3(x+1)=0

We multiply parentheses

x*3)-(-3x-3=0

Wy multiply elements

3x^2-3x-3=0

a = 3; b = -3; c = -3;
Δ = b2-4ac
Δ = -32-4·3·(-3)
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{5}}{2*3}=\frac{3-3\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{5}}{2*3}=\frac{3+3\sqrt{5}}{6}
$