5(x+3)-1/2x=33

Solution for 5(x+3)-1/2x=33 equation:

5(x+3)-1/2x=33

We move all terms to the left:

5(x+3)-1/2x-(33)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply parentheses

5x-1/2x+15-33=0

We multiply all the terms by the denominator


5x*2x+15*2x-33*2x-1=0

Wy multiply elements

10x^2+30x-66x-1=0

We add all the numbers together, and all the variables

10x^2-36x-1=0

a = 10; b = -36; c = -1;
Δ = b2-4ac
Δ = -362-4·10·(-1)
Δ = 1336
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:

$\sqrt{\Delta}=\sqrt{1336}=\sqrt{4*334}=\sqrt{4}*\sqrt{334}=2\sqrt{334}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{334}}{2*10}=\frac{36-2\sqrt{334}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{334}}{2*10}=\frac{36+2\sqrt{334}}{20}
$