12x+15x=-18.2x+5/2x=-3

Solution for 12x+15x=-18.2x+5/2x=-3 equation:

12x+15x=-18.2x+5/2x=-3

We move all terms to the left:

12x+15x-(-18.2x+5/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

27x-(-18.2x+5/2x)=0

We get rid of parentheses

27x+18.2x-5/2x=0

We multiply all the terms by the denominator


27x*2x+(18.2x)*2x-5=0

We add all the numbers together, and all the variables

27x*2x+(+18.2x)*2x-5=0

We multiply parentheses

36x^2+27x*2x-5=0

Wy multiply elements

36x^2+54x^2-5=0

We add all the numbers together, and all the variables

90x^2-5=0

a = 90; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·90·(-5)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*90}=\frac{0-30\sqrt{2}}{180}
=-\frac{30\sqrt{2}}{180}
=-\frac{\sqrt{2}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*90}=\frac{0+30\sqrt{2}}{180}
=\frac{30\sqrt{2}}{180}
=\frac{\sqrt{2}}{6}
$