8x-25=1/29x+34

Solution for 8x-25=1/29x+34 equation:

8x-25=1/29x+34

We move all terms to the left:

8x-25-(1/29x+34)=0


Domain of the equation: 29x+34)!=0

x∈R


We get rid of parentheses

8x-1/29x-34-25=0

We multiply all the terms by the denominator


8x*29x-34*29x-25*29x-1=0

Wy multiply elements

232x^2-986x-725x-1=0

We add all the numbers together, and all the variables

232x^2-1711x-1=0

a = 232; b = -1711; c = -1;
Δ = b2-4ac
Δ = -17112-4·232·(-1)
Δ = 2928449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1711)-\sqrt{2928449}}{2*232}=\frac{1711-\sqrt{2928449}}{464}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1711)+\sqrt{2928449}}{2*232}=\frac{1711+\sqrt{2928449}}{464}
$