12(x+8)+3/2x=10

Solution for 12(x+8)+3/2x=10 equation:

12(x+8)+3/2x=10

We move all terms to the left:

12(x+8)+3/2x-(10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply parentheses

12x+3/2x+96-10=0

We multiply all the terms by the denominator


12x*2x+96*2x-10*2x+3=0

Wy multiply elements

24x^2+192x-20x+3=0

We add all the numbers together, and all the variables

24x^2+172x+3=0

a = 24; b = 172; c = +3;
Δ = b2-4ac
Δ = 1722-4·24·3
Δ = 29296
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:

$\sqrt{\Delta}=\sqrt{29296}=\sqrt{16*1831}=\sqrt{16}*\sqrt{1831}=4\sqrt{1831}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(172)-4\sqrt{1831}}{2*24}=\frac{-172-4\sqrt{1831}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(172)+4\sqrt{1831}}{2*24}=\frac{-172+4\sqrt{1831}}{48}
$