26x=25/2x+27

Solution for 26x=25/2x+27 equation:

26x=25/2x+27

We move all terms to the left:

26x-(25/2x+27)=0


Domain of the equation: 2x+27)!=0

x∈R


We get rid of parentheses

26x-25/2x-27=0

We multiply all the terms by the denominator


26x*2x-27*2x-25=0

Wy multiply elements

52x^2-54x-25=0

a = 52; b = -54; c = -25;
Δ = b2-4ac
Δ = -542-4·52·(-25)
Δ = 8116
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:

$\sqrt{\Delta}=\sqrt{8116}=\sqrt{4*2029}=\sqrt{4}*\sqrt{2029}=2\sqrt{2029}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{2029}}{2*52}=\frac{54-2\sqrt{2029}}{104}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{2029}}{2*52}=\frac{54+2\sqrt{2029}}{104}
$