(2/3)x-1=27/8

Solution for (2/3)x-1=27/8 equation:

(2/3)x-1=27/8

We move all terms to the left:

(2/3)x-1-(27/8)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/3)x-1-(+27/8)=0

We multiply parentheses

2x^2-1-(+27/8)=0

We get rid of parentheses

2x^2-1-27/8=0

We multiply all the terms by the denominator


2x^2*8-27-1*8=0

We add all the numbers together, and all the variables

2x^2*8-35=0

Wy multiply elements

16x^2-35=0

a = 16; b = 0; c = -35;
Δ = b2-4ac
Δ = 02-4·16·(-35)
Δ = 2240
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:

$\sqrt{\Delta}=\sqrt{2240}=\sqrt{64*35}=\sqrt{64}*\sqrt{35}=8\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{35}}{2*16}=\frac{0-8\sqrt{35}}{32}
=-\frac{8\sqrt{35}}{32}
=-\frac{\sqrt{35}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{35}}{2*16}=\frac{0+8\sqrt{35}}{32}
=\frac{8\sqrt{35}}{32}
=\frac{\sqrt{35}}{4}
$