3/5x-15=65x+12

Solution for 3/5x-15=65x+12 equation:

3/5x-15=65x+12

We move all terms to the left:

3/5x-15-(65x+12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-65x-12-15=0

We multiply all the terms by the denominator


-65x*5x-12*5x-15*5x+3=0

Wy multiply elements

-325x^2-60x-75x+3=0

We add all the numbers together, and all the variables

-325x^2-135x+3=0

a = -325; b = -135; c = +3;
Δ = b2-4ac
Δ = -1352-4·(-325)·3
Δ = 22125
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:

$\sqrt{\Delta}=\sqrt{22125}=\sqrt{25*885}=\sqrt{25}*\sqrt{885}=5\sqrt{885}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-5\sqrt{885}}{2*-325}=\frac{135-5\sqrt{885}}{-650}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+5\sqrt{885}}{2*-325}=\frac{135+5\sqrt{885}}{-650}
$