3x+5/4x=7.5

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

3x+5/4x=7.5

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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}
$