1/7x+6=5x-4

Solution for 1/7x+6=5x-4 equation:

1/7x+6=5x-4

We move all terms to the left:

1/7x+6-(5x-4)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

1/7x-5x+4+6=0

We multiply all the terms by the denominator


-5x*7x+4*7x+6*7x+1=0

Wy multiply elements

-35x^2+28x+42x+1=0

We add all the numbers together, and all the variables

-35x^2+70x+1=0

a = -35; b = 70; c = +1;
Δ = b2-4ac
Δ = 702-4·(-35)·1
Δ = 5040
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:

$\sqrt{\Delta}=\sqrt{5040}=\sqrt{144*35}=\sqrt{144}*\sqrt{35}=12\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-12\sqrt{35}}{2*-35}=\frac{-70-12\sqrt{35}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+12\sqrt{35}}{2*-35}=\frac{-70+12\sqrt{35}}{-70}
$