75=5x+5/2x

Solution for 75=5x+5/2x equation:

75=5x+5/2x

We move all terms to the left:

75-(5x+5/2x)=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+5/2x)+75=0

We get rid of parentheses

-5x-5/2x+75=0

We multiply all the terms by the denominator


-5x*2x+75*2x-5=0

Wy multiply elements

-10x^2+150x-5=0

a = -10; b = 150; c = -5;
Δ = b2-4ac
Δ = 1502-4·(-10)·(-5)
Δ = 22300
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:

$\sqrt{\Delta}=\sqrt{22300}=\sqrt{100*223}=\sqrt{100}*\sqrt{223}=10\sqrt{223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-10\sqrt{223}}{2*-10}=\frac{-150-10\sqrt{223}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+10\sqrt{223}}{2*-10}=\frac{-150+10\sqrt{223}}{-20}
$