(8/7x)-6=x+7

Solution for (8/7x)-6=x+7 equation:

(8/7x)-6=x+7

We move all terms to the left:

(8/7x)-6-(x+7)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+8/7x)-(x+7)-6=0

We get rid of parentheses

8/7x-x-7-6=0

We multiply all the terms by the denominator


-x*7x-7*7x-6*7x+8=0

Wy multiply elements

-7x^2-49x-42x+8=0

We add all the numbers together, and all the variables

-7x^2-91x+8=0

a = -7; b = -91; c = +8;
Δ = b2-4ac
Δ = -912-4·(-7)·8
Δ = 8505
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:

$\sqrt{\Delta}=\sqrt{8505}=\sqrt{81*105}=\sqrt{81}*\sqrt{105}=9\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-91)-9\sqrt{105}}{2*-7}=\frac{91-9\sqrt{105}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-91)+9\sqrt{105}}{2*-7}=\frac{91+9\sqrt{105}}{-14}
$