45+25/6x=2x+50

Solution for 45+25/6x=2x+50 equation:

45+25/6x=2x+50

We move all terms to the left:

45+25/6x-(2x+50)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

25/6x-2x-50+45=0

We multiply all the terms by the denominator


-2x*6x-50*6x+45*6x+25=0

Wy multiply elements

-12x^2-300x+270x+25=0

We add all the numbers together, and all the variables

-12x^2-30x+25=0

a = -12; b = -30; c = +25;
Δ = b2-4ac
Δ = -302-4·(-12)·25
Δ = 2100
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:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{21}}{2*-12}=\frac{30-10\sqrt{21}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{21}}{2*-12}=\frac{30+10\sqrt{21}}{-24}
$