264r+264(r+14)=11r(r+14)

Solution for 264r+264(r+14)=11r(r+14) equation:

264r+264(r+14)=11r(r+14)

We move all terms to the left:

264r+264(r+14)-(11r(r+14))=0

We multiply parentheses

264r+264r-(11r(r+14))+3696=0


We calculate terms in parentheses: -(11r(r+14)), so:

11r(r+14)

We multiply parentheses

11r^2+154r

Back to the equation:

-(11r^2+154r)


We add all the numbers together, and all the variables

528r-(11r^2+154r)+3696=0

We get rid of parentheses

-11r^2+528r-154r+3696=0

We add all the numbers together, and all the variables

-11r^2+374r+3696=0

a = -11; b = 374; c = +3696;
Δ = b2-4ac
Δ = 3742-4·(-11)·3696
Δ = 302500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{302500}=550$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(374)-550}{2*-11}=\frac{-924}{-22}
=+42
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(374)+550}{2*-11}=\frac{176}{-22}
=-8
$