-5-3/7x+12=51-2x

Solution for -5-3/7x+12=51-2x equation:

-5-3/7x+12=51-2x

We move all terms to the left:

-5-3/7x+12-(51-2x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-3/7x-(-2x+51)-5+12=0

We add all the numbers together, and all the variables

-3/7x-(-2x+51)+7=0

We get rid of parentheses

-3/7x+2x-51+7=0

We multiply all the terms by the denominator


2x*7x-51*7x+7*7x-3=0

Wy multiply elements

14x^2-357x+49x-3=0

We add all the numbers together, and all the variables

14x^2-308x-3=0

a = 14; b = -308; c = -3;
Δ = b2-4ac
Δ = -3082-4·14·(-3)
Δ = 95032
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:

$\sqrt{\Delta}=\sqrt{95032}=\sqrt{4*23758}=\sqrt{4}*\sqrt{23758}=2\sqrt{23758}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-308)-2\sqrt{23758}}{2*14}=\frac{308-2\sqrt{23758}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-308)+2\sqrt{23758}}{2*14}=\frac{308+2\sqrt{23758}}{28}
$