6/7x+12x=60

Solution for 6/7x+12x=60 equation:

6/7x+12x=60

We move all terms to the left:

6/7x+12x-(60)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

12x+6/7x-60=0

We multiply all the terms by the denominator


12x*7x-60*7x+6=0

Wy multiply elements

84x^2-420x+6=0

a = 84; b = -420; c = +6;
Δ = b2-4ac
Δ = -4202-4·84·6
Δ = 174384
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:

$\sqrt{\Delta}=\sqrt{174384}=\sqrt{144*1211}=\sqrt{144}*\sqrt{1211}=12\sqrt{1211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-12\sqrt{1211}}{2*84}=\frac{420-12\sqrt{1211}}{168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+12\sqrt{1211}}{2*84}=\frac{420+12\sqrt{1211}}{168}
$