7/8*x=64

Solution for 7/8*x=64 equation:

7/8*x=64

We move all terms to the left:

7/8*x-(64)=0


Domain of the equation: 8*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-64*8*x+7=0

Wy multiply elements

-512x*x+7=0

Wy multiply elements

-512x^2+7=0

a = -512; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-512)·7
Δ = 14336
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:

$\sqrt{\Delta}=\sqrt{14336}=\sqrt{1024*14}=\sqrt{1024}*\sqrt{14}=32\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{14}}{2*-512}=\frac{0-32\sqrt{14}}{-1024}
=-\frac{32\sqrt{14}}{-1024}
=-\frac{\sqrt{14}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{14}}{2*-512}=\frac{0+32\sqrt{14}}{-1024}
=\frac{32\sqrt{14}}{-1024}
=\frac{\sqrt{14}}{-32}
$