-5(x/2+16)-16=3/2x

Solution for -5(x/2+16)-16=3/2x equation:

-5(x/2+16)-16=3/2x

We move all terms to the left:

-5(x/2+16)-16-(3/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-5(x/2+16)-(+3/2x)-16=0

We multiply parentheses

-5x-(+3/2x)-80-16=0

We get rid of parentheses

-5x-3/2x-80-16=0

We multiply all the terms by the denominator


-5x*2x-80*2x-16*2x-3=0

Wy multiply elements

-10x^2-160x-32x-3=0

We add all the numbers together, and all the variables

-10x^2-192x-3=0

a = -10; b = -192; c = -3;
Δ = b2-4ac
Δ = -1922-4·(-10)·(-3)
Δ = 36744
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:

$\sqrt{\Delta}=\sqrt{36744}=\sqrt{4*9186}=\sqrt{4}*\sqrt{9186}=2\sqrt{9186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-2\sqrt{9186}}{2*-10}=\frac{192-2\sqrt{9186}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+2\sqrt{9186}}{2*-10}=\frac{192+2\sqrt{9186}}{-20}
$