x.3(x+1)-5=5x-2

Solution for x.3(x+1)-5=5x-2 equation:

x.3(x+1)-5=5x-2

We move all terms to the left:

x.3(x+1)-5-(5x-2)=0

We multiply parentheses

x^2+x-(5x-2)-5=0

We get rid of parentheses

x^2+x-5x+2-5=0

We add all the numbers together, and all the variables

x^2-4x-3=0

a = 1; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·1·(-3)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{7}}{2*1}=\frac{4-2\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{7}}{2*1}=\frac{4+2\sqrt{7}}{2}
$