4r=(4r+7)(r-2)

Solution for 4r=(4r+7)(r-2) equation:

4r=(4r+7)(r-2)

We move all terms to the left:

4r-((4r+7)(r-2))=0

We multiply parentheses ..

-((+4r^2-8r+7r-14))+4r=0


We calculate terms in parentheses: -((+4r^2-8r+7r-14)), so:

(+4r^2-8r+7r-14)

We get rid of parentheses

4r^2-8r+7r-14

We add all the numbers together, and all the variables

4r^2-1r-14

Back to the equation:

-(4r^2-1r-14)


We add all the numbers together, and all the variables

4r-(4r^2-1r-14)=0

We get rid of parentheses

-4r^2+4r+1r+14=0

We add all the numbers together, and all the variables

-4r^2+5r+14=0

a = -4; b = 5; c = +14;
Δ = b2-4ac
Δ = 52-4·(-4)·14
Δ = 249
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{-(5)-\sqrt{249}}{2*-4}=\frac{-5-\sqrt{249}}{-8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{249}}{2*-4}=\frac{-5+\sqrt{249}}{-8}
$