7.5=3x+5/4x

Solution for 7.5=3x+5/4x equation:

7.5=3x+5/4x

We move all terms to the left:

7.5-(3x+5/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+3x+5/4x)+7.5=0

We get rid of parentheses

-3x-5/4x+7.5=0

We multiply all the terms by the denominator


-3x*4x+(7.5)*4x-5=0

We multiply parentheses

-3x*4x+30x-5=0

Wy multiply elements

-12x^2+30x-5=0

a = -12; b = 30; c = -5;
Δ = b2-4ac
Δ = 302-4·(-12)·(-5)
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{165}}{2*-12}=\frac{-30-2\sqrt{165}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{165}}{2*-12}=\frac{-30+2\sqrt{165}}{-24}
$