2(8/7)x=64/7

Solution for 2(8/7)x=64/7 equation:

2(8/7)x=64/7

We move all terms to the left:

2(8/7)x-(64/7)=0


Domain of the equation: 7)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2(+8/7)x-(+64/7)=0

We multiply parentheses

16x^2-(+64/7)=0

We get rid of parentheses

16x^2-64/7=0

We multiply all the terms by the denominator


16x^2*7-64=0

Wy multiply elements

112x^2-64=0

a = 112; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·112·(-64)
Δ = 28672
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:

$\sqrt{\Delta}=\sqrt{28672}=\sqrt{4096*7}=\sqrt{4096}*\sqrt{7}=64\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{7}}{2*112}=\frac{0-64\sqrt{7}}{224}
=-\frac{64\sqrt{7}}{224}
=-\frac{2\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{7}}{2*112}=\frac{0+64\sqrt{7}}{224}
=\frac{64\sqrt{7}}{224}
=\frac{2\sqrt{7}}{7}
$