7(1/8)x-3/4=20

Solution for 7(1/8)x-3/4=20 equation:

7(1/8)x-3/4=20

We move all terms to the left:

7(1/8)x-3/4-(20)=0


Domain of the equation: 8)x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
7(1/8)x-20-3/4=0

We add all the numbers together, and all the variables

7(+1/8)x-20-3/4=0

We multiply parentheses

7x^2-20-3/4=0

We multiply all the terms by the denominator


7x^2*4-3-20*4=0

We add all the numbers together, and all the variables

7x^2*4-83=0

Wy multiply elements

28x^2-83=0

a = 28; b = 0; c = -83;
Δ = b2-4ac
Δ = 02-4·28·(-83)
Δ = 9296
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:

$\sqrt{\Delta}=\sqrt{9296}=\sqrt{16*581}=\sqrt{16}*\sqrt{581}=4\sqrt{581}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{581}}{2*28}=\frac{0-4\sqrt{581}}{56}
=-\frac{4\sqrt{581}}{56}
=-\frac{\sqrt{581}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{581}}{2*28}=\frac{0+4\sqrt{581}}{56}
=\frac{4\sqrt{581}}{56}
=\frac{\sqrt{581}}{14}
$