3(0.5x-8)=3/2x-1.4

Solution for 3(0.5x-8)=3/2x-1.4 equation:

3(0.5x-8)=3/2x-1.4

We move all terms to the left:

3(0.5x-8)-(3/2x-1.4)=0


Domain of the equation: 2x-1.4)!=0

x∈R


We multiply parentheses

0x-(3/2x-1.4)-24=0

We get rid of parentheses

0x-3/2x+1.4-24=0

We multiply all the terms by the denominator


0x*2x+(1.4)*2x-24*2x-3=0

We multiply parentheses

0x*2x+2.8x-24*2x-3=0

Wy multiply elements

0x^2+2.8x-48x-3=0

We add all the numbers together, and all the variables

x^2-45.2x-3=0

a = 1; b = -45.2; c = -3;
Δ = b2-4ac
Δ = -45.22-4·1·(-3)
Δ = 2055.04
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{-(-45.2)-\sqrt{2055.04}}{2*1}=\frac{45.2-\sqrt{2055.04}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45.2)+\sqrt{2055.04}}{2*1}=\frac{45.2+\sqrt{2055.04}}{2}
$