3x-15=6/5x+12

Solution for 3x-15=6/5x+12 equation:

3x-15=6/5x+12

We move all terms to the left:

3x-15-(6/5x+12)=0


Domain of the equation: 5x+12)!=0

x∈R


We get rid of parentheses

3x-6/5x-12-15=0

We multiply all the terms by the denominator


3x*5x-12*5x-15*5x-6=0

Wy multiply elements

15x^2-60x-75x-6=0

We add all the numbers together, and all the variables

15x^2-135x-6=0

a = 15; b = -135; c = -6;
Δ = b2-4ac
Δ = -1352-4·15·(-6)
Δ = 18585
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:

$\sqrt{\Delta}=\sqrt{18585}=\sqrt{9*2065}=\sqrt{9}*\sqrt{2065}=3\sqrt{2065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-3\sqrt{2065}}{2*15}=\frac{135-3\sqrt{2065}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+3\sqrt{2065}}{2*15}=\frac{135+3\sqrt{2065}}{30}
$