5(r-3)=10(1/2r-3)

Solution for 5(r-3)=10(1/2r-3) equation:

5(r-3)=10(1/2r-3)

We move all terms to the left:

5(r-3)-(10(1/2r-3))=0


Domain of the equation: 2r-3))!=0

r∈R


We multiply parentheses

5r-(10(1/2r-3))-15=0

We multiply all the terms by the denominator


5r*2r-15*2r-3))-(10(1-3))=0

We add all the numbers together, and all the variables

5r*2r-15*2r-3))-(10(-2))=0

We add all the numbers together, and all the variables

5r*2r-15*2r=0

Wy multiply elements

10r^2-30r=0

a = 10; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·10·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*10}=\frac{0}{20}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*10}=\frac{60}{20}
=3
$