2/7x-2=28-4x

Solution for 2/7x-2=28-4x equation:

2/7x-2=28-4x

We move all terms to the left:

2/7x-2-(28-4x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

2/7x-(-4x+28)-2=0

We get rid of parentheses

2/7x+4x-28-2=0

We multiply all the terms by the denominator


4x*7x-28*7x-2*7x+2=0

Wy multiply elements

28x^2-196x-14x+2=0

We add all the numbers together, and all the variables

28x^2-210x+2=0

a = 28; b = -210; c = +2;
Δ = b2-4ac
Δ = -2102-4·28·2
Δ = 43876
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:

$\sqrt{\Delta}=\sqrt{43876}=\sqrt{4*10969}=\sqrt{4}*\sqrt{10969}=2\sqrt{10969}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-2\sqrt{10969}}{2*28}=\frac{210-2\sqrt{10969}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+2\sqrt{10969}}{2*28}=\frac{210+2\sqrt{10969}}{56}
$