3/7x-15/7x+2=6-4x

Solution for 3/7x-15/7x+2=6-4x equation:

3/7x-15/7x+2=6-4x

We move all terms to the left:

3/7x-15/7x+2-(6-4x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

3/7x-15/7x-(-4x+6)+2=0

We get rid of parentheses

3/7x-15/7x+4x-6+2=0

We multiply all the terms by the denominator


4x*7x-6*7x+2*7x+3-15=0

We add all the numbers together, and all the variables

4x*7x-6*7x+2*7x-12=0

Wy multiply elements

28x^2-42x+14x-12=0

We add all the numbers together, and all the variables

28x^2-28x-12=0

a = 28; b = -28; c = -12;
Δ = b2-4ac
Δ = -282-4·28·(-12)
Δ = 2128
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:

$\sqrt{\Delta}=\sqrt{2128}=\sqrt{16*133}=\sqrt{16}*\sqrt{133}=4\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{133}}{2*28}=\frac{28-4\sqrt{133}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{133}}{2*28}=\frac{28+4\sqrt{133}}{56}
$