(6/7)+(1/8)x=2

Solution for (6/7)+(1/8)x=2 equation:

(6/7)+(1/8)x=2

We move all terms to the left:

(6/7)+(1/8)x-(2)=0


Domain of the equation: 8)x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
(1/8)x-2+(6/7)=0

We add all the numbers together, and all the variables

(+1/8)x-2+(+6/7)=0

We multiply parentheses

x^2-2+(+6/7)=0

We get rid of parentheses

x^2-2+6/7=0

We multiply all the terms by the denominator


x^2*7+6-2*7=0

We add all the numbers together, and all the variables

x^2*7-8=0

Wy multiply elements

7x^2-8=0

a = 7; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·7·(-8)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{14}}{2*7}=\frac{0-4\sqrt{14}}{14}
=-\frac{4\sqrt{14}}{14}
=-\frac{2\sqrt{14}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{14}}{2*7}=\frac{0+4\sqrt{14}}{14}
=\frac{4\sqrt{14}}{14}
=\frac{2\sqrt{14}}{7}
$