4r(6r+5)=16-9r

Solution for 4r(6r+5)=16-9r equation:

4r(6r+5)=16-9r

We move all terms to the left:

4r(6r+5)-(16-9r)=0

We add all the numbers together, and all the variables

4r(6r+5)-(-9r+16)=0

We multiply parentheses

24r^2+20r-(-9r+16)=0

We get rid of parentheses

24r^2+20r+9r-16=0

We add all the numbers together, and all the variables

24r^2+29r-16=0

a = 24; b = 29; c = -16;
Δ = b2-4ac
Δ = 292-4·24·(-16)
Δ = 2377
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{-(29)-\sqrt{2377}}{2*24}=\frac{-29-\sqrt{2377}}{48}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{2377}}{2*24}=\frac{-29+\sqrt{2377}}{48}
$