.5(x+8)+3/2x=10

Solution for .5(x+8)+3/2x=10 equation:

.5(x+8)+3/2x=10

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply parentheses

0.5x+3/2x+4-10=0

We multiply all the terms by the denominator


(0.5x)*2x+4*2x-10*2x+3=0

We add all the numbers together, and all the variables

(+0.5x)*2x+4*2x-10*2x+3=0

We multiply parentheses

0x^2+4*2x-10*2x+3=0

Wy multiply elements

0x^2+8x-20x+3=0

We add all the numbers together, and all the variables

x^2-12x+3=0

a = 1; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·1·3
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{33}}{2*1}=\frac{12-2\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{33}}{2*1}=\frac{12+2\sqrt{33}}{2}
$