3(x-5)=5(1/2x-1)

Solution for 3(x-5)=5(1/2x-1) equation:

3(x-5)=5(1/2x-1)

We move all terms to the left:

3(x-5)-(5(1/2x-1))=0


Domain of the equation: 2x-1))!=0

x∈R


We multiply parentheses

3x-(5(1/2x-1))-15=0

We multiply all the terms by the denominator


3x*2x-15*2x-1))-(5(1-1))=0

We add all the numbers together, and all the variables

3x*2x-15*2x-1))-(50)=0

We add all the numbers together, and all the variables

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

Wy multiply elements

6x^2-30x=0

a = 6; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·6·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*6}=\frac{60}{12}
=5
$