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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} $
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