45+2(5/6)x=2x+50

Solution for 45+2(5/6)x=2x+50 equation:

45+2(5/6)x=2x+50

We move all terms to the left:

45+2(5/6)x-(2x+50)=0


Domain of the equation: 6)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2(+5/6)x-(2x+50)+45=0

We multiply parentheses

10x^2-(2x+50)+45=0

We get rid of parentheses

10x^2-2x-50+45=0

We add all the numbers together, and all the variables

10x^2-2x-5=0

a = 10; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·10·(-5)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{51}}{2*10}=\frac{2-2\sqrt{51}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{51}}{2*10}=\frac{2+2\sqrt{51}}{20}
$