(5r+11)(r-2)=-(9r-18)

Solution for (5r+11)(r-2)=-(9r-18) equation:

(5r+11)(r-2)=-(9r-18)

We move all terms to the left:

(5r+11)(r-2)-(-(9r-18))=0

We multiply parentheses ..

(+5r^2-10r+11r-22)-(-(9r-18))=0


We calculate terms in parentheses: -(-(9r-18)), so:

-(9r-18)

We get rid of parentheses

-9r+18

Back to the equation:

-(-9r+18)


We get rid of parentheses

5r^2-10r+11r+9r-22-18=0

We add all the numbers together, and all the variables

5r^2+10r-40=0

a = 5; b = 10; c = -40;
Δ = b2-4ac
Δ = 102-4·5·(-40)
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{-(10)-30}{2*5}=\frac{-40}{10}
=-4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+30}{2*5}=\frac{20}{10}
=2
$