12x-15=6-7/5x

Solution for 12x-15=6-7/5x equation:

12x-15=6-7/5x

We move all terms to the left:

12x-15-(6-7/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

12x-(-7/5x+6)-15=0

We get rid of parentheses

12x+7/5x-6-15=0

We multiply all the terms by the denominator


12x*5x-6*5x-15*5x+7=0

Wy multiply elements

60x^2-30x-75x+7=0

We add all the numbers together, and all the variables

60x^2-105x+7=0

a = 60; b = -105; c = +7;
Δ = b2-4ac
Δ = -1052-4·60·7
Δ = 9345
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{-(-105)-\sqrt{9345}}{2*60}=\frac{105-\sqrt{9345}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{9345}}{2*60}=\frac{105+\sqrt{9345}}{120}
$