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

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

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

We move all terms to the left:

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


Domain of the equation: 2x-30)!=0

x∈R


We multiply parentheses

0x-(3/2x-30)-12=0

We get rid of parentheses

0x-3/2x+30-12=0

We multiply all the terms by the denominator


0x*2x+30*2x-12*2x-3=0

Wy multiply elements

0x^2+60x-24x-3=0

We add all the numbers together, and all the variables

x^2+36x-3=0

a = 1; b = 36; c = -3;
Δ = b2-4ac
Δ = 362-4·1·(-3)
Δ = 1308
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:

$\sqrt{\Delta}=\sqrt{1308}=\sqrt{4*327}=\sqrt{4}*\sqrt{327}=2\sqrt{327}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{327}}{2*1}=\frac{-36-2\sqrt{327}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{327}}{2*1}=\frac{-36+2\sqrt{327}}{2}
$