75=x+2/3x+x-5

Solution for 75=x+2/3x+x-5 equation:

75=x+2/3x+x-5

We move all terms to the left:

75-(x+2/3x+x-5)=0


Domain of the equation: 3x+x-5)!=0

x∈R


We add all the numbers together, and all the variables

-(2x+2/3x-5)+75=0

We get rid of parentheses

-2x-2/3x+5+75=0

We multiply all the terms by the denominator


-2x*3x+5*3x+75*3x-2=0

Wy multiply elements

-6x^2+15x+225x-2=0

We add all the numbers together, and all the variables

-6x^2+240x-2=0

a = -6; b = 240; c = -2;
Δ = b2-4ac
Δ = 2402-4·(-6)·(-2)
Δ = 57552
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:

$\sqrt{\Delta}=\sqrt{57552}=\sqrt{16*3597}=\sqrt{16}*\sqrt{3597}=4\sqrt{3597}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-4\sqrt{3597}}{2*-6}=\frac{-240-4\sqrt{3597}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+4\sqrt{3597}}{2*-6}=\frac{-240+4\sqrt{3597}}{-12}
$