3/4x-6=2x-47

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Solution for 3/4x-6=2x-47 equation: 



3/4x-6=2x-47

We move all terms to the left:

3/4x-6-(2x-47)=0



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



We get rid of parentheses

3/4x-2x+47-6=0

We multiply all the terms by the denominator


-2x*4x+47*4x-6*4x+3=0

Wy multiply elements

-8x^2+188x-24x+3=0

We add all the numbers together, and all the variables

-8x^2+164x+3=0

a = -8; b = 164; c = +3;
Δ = b2-4ac
Δ = 1642-4·(-8)·3
Δ = 26992
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:


$\sqrt{\Delta}=\sqrt{26992}=\sqrt{16*1687}=\sqrt{16}*\sqrt{1687}=4\sqrt{1687}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(164)-4\sqrt{1687}}{2*-8}=\frac{-164-4\sqrt{1687}}{-16}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(164)+4\sqrt{1687}}{2*-8}=\frac{-164+4\sqrt{1687}}{-16}
$

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