x+0.5x+(2/3)x=30-4

Solution for x+0.5x+(2/3)x=30-4 equation:

x+0.5x+(2/3)x=30-4

We move all terms to the left:

x+0.5x+(2/3)x-(30-4)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+0.5x+(+2/3)x-26=0

We add all the numbers together, and all the variables

1.5x+(+2/3)x-26=0

We multiply parentheses

2x^2+1.5x-26=0

a = 2; b = 1.5; c = -26;
Δ = b2-4ac
Δ = 1.52-4·2·(-26)
Δ = 210.25
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{-(1.5)-\sqrt{210.25}}{2*2}=\frac{-1.5-\sqrt{210.25}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{210.25}}{2*2}=\frac{-1.5+\sqrt{210.25}}{4}
$