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

Solution for 3x+(3/2+2)x-5=0 equation:

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


Domain of the equation: 2+2)x!=0

We move all terms containing x to the left, all other terms to the right

2)x!=-2

x!=-2/1

x!=-2

x∈R


We multiply parentheses

3x^2+3x+2x-5=0

We add all the numbers together, and all the variables

3x^2+5x-5=0

a = 3; b = 5; c = -5;
Δ = b2-4ac
Δ = 52-4·3·(-5)
Δ = 85
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{85}}{2*3}=\frac{-5-\sqrt{85}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{85}}{2*3}=\frac{-5+\sqrt{85}}{6}
$