180=2x-25+3/4x

Solution for 180=2x-25+3/4x equation:

180=2x-25+3/4x

We move all terms to the left:

180-(2x-25+3/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(2x+3/4x-25)+180=0

We get rid of parentheses

-2x-3/4x+25+180=0

We multiply all the terms by the denominator


-2x*4x+25*4x+180*4x-3=0

Wy multiply elements

-8x^2+100x+720x-3=0

We add all the numbers together, and all the variables

-8x^2+820x-3=0

a = -8; b = 820; c = -3;
Δ = b2-4ac
Δ = 8202-4·(-8)·(-3)
Δ = 672304
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:

$\sqrt{\Delta}=\sqrt{672304}=\sqrt{16*42019}=\sqrt{16}*\sqrt{42019}=4\sqrt{42019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(820)-4\sqrt{42019}}{2*-8}=\frac{-820-4\sqrt{42019}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(820)+4\sqrt{42019}}{2*-8}=\frac{-820+4\sqrt{42019}}{-16}
$