(51/2)x=8

Solution for (51/2)x=8 equation:

(51/2)x=8

We move all terms to the left:

(51/2)x-(8)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+51/2)x-8=0

We multiply parentheses

51x^2-8=0

a = 51; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·51·(-8)
Δ = 1632
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:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{102}}{2*51}=\frac{0-4\sqrt{102}}{102}
=-\frac{4\sqrt{102}}{102}
=-\frac{2\sqrt{102}}{51}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{102}}{2*51}=\frac{0+4\sqrt{102}}{102}
=\frac{4\sqrt{102}}{102}
=\frac{2\sqrt{102}}{51}
$