3.00x+0.50=6/00x+0.20

Solution for 3.00x+0.50=6/00x+0.20 equation:

3.00x+0.50=6/00x+0.20

We move all terms to the left:

3.00x+0.50-(6/00x+0.20)=0


Domain of the equation: 00x+0.20)!=0

x∈R


We add all the numbers together, and all the variables

3.00x-(6/00x+0.2)+0.50=0

We add all the numbers together, and all the variables

3.00x-(6/00x+0.2)+0.5=0

We get rid of parentheses

3.00x-6/00x-0.2+0.5=0

We multiply all the terms by the denominator


(3.00x)*00x-(0.2)*00x+(0.5)*00x-6=0

We add all the numbers together, and all the variables

(+3.00x)*00x-(0.2)*00x+(0.5)*00x-6=0

We multiply parentheses

0x^2-0x+0x-6=0

We add all the numbers together, and all the variables

x^2-6=0

a = 1; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·1·(-6)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*1}=\frac{0-2\sqrt{6}}{2}
=-\frac{2\sqrt{6}}{2}
=-\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*1}=\frac{0+2\sqrt{6}}{2}
=\frac{2\sqrt{6}}{2}
=\sqrt{6}
$