2x-4/7x=-20

Solution for 2x-4/7x=-20 equation:

2x-4/7x=-20

We move all terms to the left:

2x-4/7x-(-20)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

2x-4/7x+20=0

We multiply all the terms by the denominator


2x*7x+20*7x-4=0

Wy multiply elements

14x^2+140x-4=0

a = 14; b = 140; c = -4;
Δ = b2-4ac
Δ = 1402-4·14·(-4)
Δ = 19824
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:

$\sqrt{\Delta}=\sqrt{19824}=\sqrt{16*1239}=\sqrt{16}*\sqrt{1239}=4\sqrt{1239}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-4\sqrt{1239}}{2*14}=\frac{-140-4\sqrt{1239}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+4\sqrt{1239}}{2*14}=\frac{-140+4\sqrt{1239}}{28}
$