3/2x+x=-15

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

3/2x+x=-15

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/2x+15=0

We multiply all the terms by the denominator


x*2x+15*2x+3=0

Wy multiply elements

2x^2+30x+3=0

a = 2; b = 30; c = +3;
Δ = b2-4ac
Δ = 302-4·2·3
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*2}=\frac{-30-2\sqrt{219}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{219}}{2*2}=\frac{-30+2\sqrt{219}}{4}
$