x-3=49-7/6x

Solution for x-3=49-7/6x equation:

x-3=49-7/6x

We move all terms to the left:

x-3-(49-7/6x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(-7/6x+49)-3=0

We get rid of parentheses

x+7/6x-49-3=0

We multiply all the terms by the denominator


x*6x-49*6x-3*6x+7=0

Wy multiply elements

6x^2-294x-18x+7=0

We add all the numbers together, and all the variables

6x^2-312x+7=0

a = 6; b = -312; c = +7;
Δ = b2-4ac
Δ = -3122-4·6·7
Δ = 97176
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:

$\sqrt{\Delta}=\sqrt{97176}=\sqrt{4*24294}=\sqrt{4}*\sqrt{24294}=2\sqrt{24294}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-312)-2\sqrt{24294}}{2*6}=\frac{312-2\sqrt{24294}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-312)+2\sqrt{24294}}{2*6}=\frac{312+2\sqrt{24294}}{12}
$