15+1/2x=30-3x

Solution for 15+1/2x=30-3x equation:

15+1/2x=30-3x

We move all terms to the left:

15+1/2x-(30-3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-3x+30)+15=0

We get rid of parentheses

1/2x+3x-30+15=0

We multiply all the terms by the denominator


3x*2x-30*2x+15*2x+1=0

Wy multiply elements

6x^2-60x+30x+1=0

We add all the numbers together, and all the variables

6x^2-30x+1=0

a = 6; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·6·1
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{219}}{2*6}=\frac{30-2\sqrt{219}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{219}}{2*6}=\frac{30+2\sqrt{219}}{12}
$