1/2x+3.2x=20

Solution for 1/2x+3.2x=20 equation:

1/2x+3.2x=20

We move all terms to the left:

1/2x+3.2x-(20)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3.2x+1/2x-20=0

We multiply all the terms by the denominator


(3.2x)*2x-20*2x+1=0

We add all the numbers together, and all the variables

(+3.2x)*2x-20*2x+1=0

We multiply parentheses

6x^2-20*2x+1=0

Wy multiply elements

6x^2-40x+1=0

a = 6; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·6·1
Δ = 1576
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:

$\sqrt{\Delta}=\sqrt{1576}=\sqrt{4*394}=\sqrt{4}*\sqrt{394}=2\sqrt{394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{394}}{2*6}=\frac{40-2\sqrt{394}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{394}}{2*6}=\frac{40+2\sqrt{394}}{12}
$