.5(6x+10)=7(3/7x-2)

Solution for .5(6x+10)=7(3/7x-2) equation:

.5(6x+10)=7(3/7x-2)

We move all terms to the left:

.5(6x+10)-(7(3/7x-2))=0


Domain of the equation: 7x-2))!=0

x∈R


We multiply parentheses

3x-(7(3/7x-2))+5=0

We multiply all the terms by the denominator


3x*7x+5*7x-2))-(7(3-2))=0

We add all the numbers together, and all the variables

3x*7x+5*7x-2))-(71)=0

We add all the numbers together, and all the variables

3x*7x+5*7x=0

Wy multiply elements

21x^2+35x=0

a = 21; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·21·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*21}=\frac{-70}{42}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*21}=\frac{0}{42}
=0
$