(7/8)x=1/2

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

(7/8)x=1/2

We move all terms to the left:

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


Domain of the equation: 8)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

7x^2-1/2=0

We multiply all the terms by the denominator


7x^2*2-1=0

Wy multiply elements

14x^2-1=0

a = 14; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·14·(-1)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{14}}{2*14}=\frac{0-2\sqrt{14}}{28}
=-\frac{2\sqrt{14}}{28}
=-\frac{\sqrt{14}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{14}}{2*14}=\frac{0+2\sqrt{14}}{28}
=\frac{2\sqrt{14}}{28}
=\frac{\sqrt{14}}{14}
$