x/2x+10=7x-10

Solution for x/2x+10=7x-10 equation:

x/2x+10=7x-10

We move all terms to the left:

x/2x+10-(7x-10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

x/2x-7x+10+10=0

We multiply all the terms by the denominator


x-7x*2x+10*2x+10*2x=0

Wy multiply elements

-14x^2+x+20x+20x=0

We add all the numbers together, and all the variables

-14x^2+41x=0

a = -14; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-14)·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*-14}=\frac{-82}{-28}
=2+13/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-14}=\frac{0}{-28}
=0
$