10x-29=4+2/7x+1

Solution for 10x-29=4+2/7x+1 equation:

10x-29=4+2/7x+1

We move all terms to the left:

10x-29-(4+2/7x+1)=0


Domain of the equation: 7x+1)!=0

x∈R


We add all the numbers together, and all the variables

10x-(2/7x+5)-29=0

We get rid of parentheses

10x-2/7x-5-29=0

We multiply all the terms by the denominator


10x*7x-5*7x-29*7x-2=0

Wy multiply elements

70x^2-35x-203x-2=0

We add all the numbers together, and all the variables

70x^2-238x-2=0

a = 70; b = -238; c = -2;
Δ = b2-4ac
Δ = -2382-4·70·(-2)
Δ = 57204
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:

$\sqrt{\Delta}=\sqrt{57204}=\sqrt{36*1589}=\sqrt{36}*\sqrt{1589}=6\sqrt{1589}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-238)-6\sqrt{1589}}{2*70}=\frac{238-6\sqrt{1589}}{140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-238)+6\sqrt{1589}}{2*70}=\frac{238+6\sqrt{1589}}{140}
$