0.2x+1/2x=7

Solution for 0.2x+1/2x=7 equation:

0.2x+1/2x=7

We move all terms to the left:

0.2x+1/2x-(7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


(0.2x)*2x-7*2x+1=0

We add all the numbers together, and all the variables

(+0.2x)*2x-7*2x+1=0

We multiply parentheses

0x^2-7*2x+1=0

Wy multiply elements

0x^2-14x+1=0

We add all the numbers together, and all the variables

x^2-14x+1=0

a = 1; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·1·1
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-8\sqrt{3}}{2*1}=\frac{14-8\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+8\sqrt{3}}{2*1}=\frac{14+8\sqrt{3}}{2}
$