11.3(r/5-5)=-2/5r-20

Solution for 11.3(r/5-5)=-2/5r-20 equation:

11.3(r/5-5)=-2/5r-20

We move all terms to the left:

11.3(r/5-5)-(-2/5r-20)=0


Domain of the equation: 5r-20)!=0

r∈R


We multiply parentheses

11.3r-(-2/5r-20)-56.5=0

We get rid of parentheses

11.3r+2/5r+20-56.5=0

We multiply all the terms by the denominator


(11.3r)*5r+20*5r-(56.5)*5r+2=0

We add all the numbers together, and all the variables

(+11.3r)*5r+20*5r-(56.5)*5r+2=0

We multiply parentheses

55r^2+20*5r-282.5r+2=0

Wy multiply elements

55r^2+100r-282.5r+2=0

We add all the numbers together, and all the variables

55r^2-182.5r+2=0

a = 55; b = -182.5; c = +2;
Δ = b2-4ac
Δ = -182.52-4·55·2
Δ = 32866.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-182.5)-\sqrt{32866.25}}{2*55}=\frac{182.5-\sqrt{32866.25}}{110}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-182.5)+\sqrt{32866.25}}{2*55}=\frac{182.5+\sqrt{32866.25}}{110}
$