4.25x+1/2x=40-2x

Solution for 4.25x+1/2x=40-2x equation:

4.25x+1/2x=40-2x

We move all terms to the left:

4.25x+1/2x-(40-2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4.25x+1/2x-(-2x+40)=0

We get rid of parentheses

4.25x+1/2x+2x-40=0

We multiply all the terms by the denominator


(4.25x)*2x+2x*2x-40*2x+1=0

We add all the numbers together, and all the variables

(+4.25x)*2x+2x*2x-40*2x+1=0

We multiply parentheses

8x^2+2x*2x-40*2x+1=0

Wy multiply elements

8x^2+4x^2-80x+1=0

We add all the numbers together, and all the variables

12x^2-80x+1=0

a = 12; b = -80; c = +1;
Δ = b2-4ac
Δ = -802-4·12·1
Δ = 6352
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:

$\sqrt{\Delta}=\sqrt{6352}=\sqrt{16*397}=\sqrt{16}*\sqrt{397}=4\sqrt{397}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{397}}{2*12}=\frac{80-4\sqrt{397}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{397}}{2*12}=\frac{80+4\sqrt{397}}{24}
$