x=75/2.7*x

Solution for x=75/2.7*x equation:

x=75/2.7x

We move all terms to the left:

x-(75/2.7x)=0


Domain of the equation: 2.7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+75/2.7x)=0

We get rid of parentheses

x-75/2.7x=0

We multiply all the terms by the denominator


x*2.7x-75=0

Wy multiply elements

2x^2-75=0

a = 2; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·2·(-75)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*2}=\frac{0-10\sqrt{6}}{4}
=-\frac{10\sqrt{6}}{4}
=-\frac{5\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*2}=\frac{0+10\sqrt{6}}{4}
=\frac{10\sqrt{6}}{4}
=\frac{5\sqrt{6}}{2}
$