2x+3/4x=60

Solution for 2x+3/4x=60 equation:

2x+3/4x=60

We move all terms to the left:

2x+3/4x-(60)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


2x*4x-60*4x+3=0

Wy multiply elements

8x^2-240x+3=0

a = 8; b = -240; c = +3;
Δ = b2-4ac
Δ = -2402-4·8·3
Δ = 57504
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:

$\sqrt{\Delta}=\sqrt{57504}=\sqrt{16*3594}=\sqrt{16}*\sqrt{3594}=4\sqrt{3594}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-4\sqrt{3594}}{2*8}=\frac{240-4\sqrt{3594}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+4\sqrt{3594}}{2*8}=\frac{240+4\sqrt{3594}}{16}
$