x-7=-3(x+1)/5

Solution for x-7=-3(x+1)/5 equation:

x-7=-3(x+1)/5

We move all terms to the left:

x-7-(-3(x+1)/5)=0

We multiply all the terms by the denominator


x*5)-(-3(x+1)-7*5)=0

We add all the numbers together, and all the variables

x*5)-(-3(x+1)=0

We multiply parentheses

x*5)-(-3x-3=0

Wy multiply elements

5x^2-3x-3=0

a = 5; b = -3; c = -3;
Δ = b2-4ac
Δ = -32-4·5·(-3)
Δ = 69
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{-(-3)-\sqrt{69}}{2*5}=\frac{3-\sqrt{69}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{69}}{2*5}=\frac{3+\sqrt{69}}{10}
$