1/29x+25=4x+17

Solution for 1/29x+25=4x+17 equation:

1/29x+25=4x+17

We move all terms to the left:

1/29x+25-(4x+17)=0


Domain of the equation: 29x!=0

x!=0/29

x!=0

x∈R


We get rid of parentheses

1/29x-4x-17+25=0

We multiply all the terms by the denominator


-4x*29x-17*29x+25*29x+1=0

Wy multiply elements

-116x^2-493x+725x+1=0

We add all the numbers together, and all the variables

-116x^2+232x+1=0

a = -116; b = 232; c = +1;
Δ = b2-4ac
Δ = 2322-4·(-116)·1
Δ = 54288
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:

$\sqrt{\Delta}=\sqrt{54288}=\sqrt{144*377}=\sqrt{144}*\sqrt{377}=12\sqrt{377}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(232)-12\sqrt{377}}{2*-116}=\frac{-232-12\sqrt{377}}{-232}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(232)+12\sqrt{377}}{2*-116}=\frac{-232+12\sqrt{377}}{-232}
$