1/28x+12=3x-4

Solution for 1/28x+12=3x-4 equation:

1/28x+12=3x-4

We move all terms to the left:

1/28x+12-(3x-4)=0


Domain of the equation: 28x!=0

x!=0/28

x!=0

x∈R


We get rid of parentheses

1/28x-3x+4+12=0

We multiply all the terms by the denominator


-3x*28x+4*28x+12*28x+1=0

Wy multiply elements

-84x^2+112x+336x+1=0

We add all the numbers together, and all the variables

-84x^2+448x+1=0

a = -84; b = 448; c = +1;
Δ = b2-4ac
Δ = 4482-4·(-84)·1
Δ = 201040
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:

$\sqrt{\Delta}=\sqrt{201040}=\sqrt{16*12565}=\sqrt{16}*\sqrt{12565}=4\sqrt{12565}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(448)-4\sqrt{12565}}{2*-84}=\frac{-448-4\sqrt{12565}}{-168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(448)+4\sqrt{12565}}{2*-84}=\frac{-448+4\sqrt{12565}}{-168}
$