5x+(13/2x)+264=410

Solution for 5x+(13/2x)+264=410 equation:

5x+(13/2x)+264=410

We move all terms to the left:

5x+(13/2x)+264-(410)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x+(+13/2x)+264-410=0

We add all the numbers together, and all the variables

5x+(+13/2x)-146=0

We get rid of parentheses

5x+13/2x-146=0

We multiply all the terms by the denominator


5x*2x-146*2x+13=0

Wy multiply elements

10x^2-292x+13=0

a = 10; b = -292; c = +13;
Δ = b2-4ac
Δ = -2922-4·10·13
Δ = 84744
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:

$\sqrt{\Delta}=\sqrt{84744}=\sqrt{36*2354}=\sqrt{36}*\sqrt{2354}=6\sqrt{2354}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-292)-6\sqrt{2354}}{2*10}=\frac{292-6\sqrt{2354}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-292)+6\sqrt{2354}}{2*10}=\frac{292+6\sqrt{2354}}{20}
$