3/4x+5-12x=15

Solution for 3/4x+5-12x=15 equation:

3/4x+5-12x=15

We move all terms to the left:

3/4x+5-12x-(15)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-12x+3/4x-10=0

We multiply all the terms by the denominator


-12x*4x-10*4x+3=0

Wy multiply elements

-48x^2-40x+3=0

a = -48; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·(-48)·3
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{34}}{2*-48}=\frac{40-8\sqrt{34}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{34}}{2*-48}=\frac{40+8\sqrt{34}}{-96}
$