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

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

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

We move all terms to the left:

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

x*5)-(-9x-3=0

Wy multiply elements

5x^2-9x-3=0

a = 5; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·5·(-3)
Δ = 141
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{-(-9)-\sqrt{141}}{2*5}=\frac{9-\sqrt{141}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{141}}{2*5}=\frac{9+\sqrt{141}}{10}
$