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

Solution for (x+5)*3=(x-5)*3x equation:

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

We move all terms to the left:

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

We multiply parentheses

3x-((x-5)*3x)+15=0


We calculate terms in parentheses: -((x-5)*3x), so:

(x-5)*3x

We multiply parentheses

3x^2-15x

Back to the equation:

-(3x^2-15x)


We get rid of parentheses

-3x^2+3x+15x+15=0

We add all the numbers together, and all the variables

-3x^2+18x+15=0

a = -3; b = 18; c = +15;
Δ = b2-4ac
Δ = 182-4·(-3)·15
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{14}}{2*-3}=\frac{-18-6\sqrt{14}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{14}}{2*-3}=\frac{-18+6\sqrt{14}}{-6}
$