1/7x+7=2x-5

Solution for 1/7x+7=2x-5 equation:

1/7x+7=2x-5

We move all terms to the left:

1/7x+7-(2x-5)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

1/7x-2x+5+7=0

We multiply all the terms by the denominator


-2x*7x+5*7x+7*7x+1=0

Wy multiply elements

-14x^2+35x+49x+1=0

We add all the numbers together, and all the variables

-14x^2+84x+1=0

a = -14; b = 84; c = +1;
Δ = b2-4ac
Δ = 842-4·(-14)·1
Δ = 7112
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:

$\sqrt{\Delta}=\sqrt{7112}=\sqrt{4*1778}=\sqrt{4}*\sqrt{1778}=2\sqrt{1778}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-2\sqrt{1778}}{2*-14}=\frac{-84-2\sqrt{1778}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+2\sqrt{1778}}{2*-14}=\frac{-84+2\sqrt{1778}}{-28}
$