3(0.5x-5)=3/2x-1.5

Solution for 3(0.5x-5)=3/2x-1.5 equation:

3(0.5x-5)=3/2x-1.5

We move all terms to the left:

3(0.5x-5)-(3/2x-1.5)=0


Domain of the equation: 2x-1.5)!=0

x∈R


We multiply parentheses

0x-(3/2x-1.5)-15=0

We get rid of parentheses

0x-3/2x+1.5-15=0

We multiply all the terms by the denominator


0x*2x+(1.5)*2x-15*2x-3=0

We multiply parentheses

0x*2x+3x-15*2x-3=0

Wy multiply elements

0x^2+3x-30x-3=0

We add all the numbers together, and all the variables

x^2-27x-3=0

a = 1; b = -27; c = -3;
Δ = b2-4ac
Δ = -272-4·1·(-3)
Δ = 741
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{-(-27)-\sqrt{741}}{2*1}=\frac{27-\sqrt{741}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{741}}{2*1}=\frac{27+\sqrt{741}}{2}
$