7(2x+20)=4/7x

Solution for 7(2x+20)=4/7x equation:

7(2x+20)=4/7x

We move all terms to the left:

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


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

14x-(+4/7x)+140=0

We get rid of parentheses

14x-4/7x+140=0

We multiply all the terms by the denominator


14x*7x+140*7x-4=0

Wy multiply elements

98x^2+980x-4=0

a = 98; b = 980; c = -4;
Δ = b2-4ac
Δ = 9802-4·98·(-4)
Δ = 961968
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:

$\sqrt{\Delta}=\sqrt{961968}=\sqrt{784*1227}=\sqrt{784}*\sqrt{1227}=28\sqrt{1227}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(980)-28\sqrt{1227}}{2*98}=\frac{-980-28\sqrt{1227}}{196}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(980)+28\sqrt{1227}}{2*98}=\frac{-980+28\sqrt{1227}}{196}
$