1/2x+3(1/3x+5)=45

Solution for 1/2x+3(1/3x+5)=45 equation:

1/2x+3(1/3x+5)=45

We move all terms to the left:

1/2x+3(1/3x+5)-(45)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x+5)!=0

x∈R


We multiply parentheses

1/2x+3x+15-45=0

We multiply all the terms by the denominator


3x*2x+15*2x-45*2x+1=0

Wy multiply elements

6x^2+30x-90x+1=0

We add all the numbers together, and all the variables

6x^2-60x+1=0

a = 6; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·6·1
Δ = 3576
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:

$\sqrt{\Delta}=\sqrt{3576}=\sqrt{4*894}=\sqrt{4}*\sqrt{894}=2\sqrt{894}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{894}}{2*6}=\frac{60-2\sqrt{894}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{894}}{2*6}=\frac{60+2\sqrt{894}}{12}
$