3/5x-15=x+12

Solution for 3/5x-15=x+12 equation:

3/5x-15=x+12

We move all terms to the left:

3/5x-15-(x+12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-x-12-15=0

We multiply all the terms by the denominator


-x*5x-12*5x-15*5x+3=0

Wy multiply elements

-5x^2-60x-75x+3=0

We add all the numbers together, and all the variables

-5x^2-135x+3=0

a = -5; b = -135; c = +3;
Δ = b2-4ac
Δ = -1352-4·(-5)·3
Δ = 18285
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{-(-135)-\sqrt{18285}}{2*-5}=\frac{135-\sqrt{18285}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+\sqrt{18285}}{2*-5}=\frac{135+\sqrt{18285}}{-10}
$