x/7x+10=2x+35

Solution for x/7x+10=2x+35 equation:

x/7x+10=2x+35

We move all terms to the left:

x/7x+10-(2x+35)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

x/7x-2x-35+10=0

We multiply all the terms by the denominator


x-2x*7x-35*7x+10*7x=0

Wy multiply elements

-14x^2+x-245x+70x=0

We add all the numbers together, and all the variables

-14x^2-174x=0

a = -14; b = -174; c = 0;
Δ = b2-4ac
Δ = -1742-4·(-14)·0
Δ = 30276
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30276}=174$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-174)-174}{2*-14}=\frac{0}{-28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-174)+174}{2*-14}=\frac{348}{-28}
=-12+3/7
$