2x+5(3/2)x=19

Solution for 2x+5(3/2)x=19 equation:

2x+5(3/2)x=19

We move all terms to the left:

2x+5(3/2)x-(19)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x+5(+3/2)x-19=0

We multiply parentheses

15x^2+2x-19=0

a = 15; b = 2; c = -19;
Δ = b2-4ac
Δ = 22-4·15·(-19)
Δ = 1144
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:

$\sqrt{\Delta}=\sqrt{1144}=\sqrt{4*286}=\sqrt{4}*\sqrt{286}=2\sqrt{286}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{286}}{2*15}=\frac{-2-2\sqrt{286}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{286}}{2*15}=\frac{-2+2\sqrt{286}}{30}
$