0.2x+3/2x=x+30

Solution for 0.2x+3/2x=x+30 equation:

0.2x+3/2x=x+30

We move all terms to the left:

0.2x+3/2x-(x+30)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

0.2x+3/2x-x-30=0

We multiply all the terms by the denominator


(0.2x)*2x-x*2x-30*2x+3=0

We add all the numbers together, and all the variables

(+0.2x)*2x-x*2x-30*2x+3=0

We multiply parentheses

0x^2-x*2x-30*2x+3=0

Wy multiply elements

0x^2-2x^2-60x+3=0

We add all the numbers together, and all the variables

-1x^2-60x+3=0

a = -1; b = -60; c = +3;
Δ = b2-4ac
Δ = -602-4·(-1)·3
Δ = 3612
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:

$\sqrt{\Delta}=\sqrt{3612}=\sqrt{4*903}=\sqrt{4}*\sqrt{903}=2\sqrt{903}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{903}}{2*-1}=\frac{60-2\sqrt{903}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{903}}{2*-1}=\frac{60+2\sqrt{903}}{-2}
$