/2x+3x=45

Solution for /2x+3x=45 equation:

/2x+3x=45

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+/2x-45=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x*2x-45*2x=0

Wy multiply elements

6x^2-90x=0

a = 6; b = -90; c = 0;
Δ = b2-4ac
Δ = -902-4·6·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90}{2*6}=\frac{180}{12}
=15
$