(3r+4)(8r-2)=90

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Solution for (3r+4)(8r-2)=90 equation:



(3r+4)(8r-2)=90
We move all terms to the left:
(3r+4)(8r-2)-(90)=0
We multiply parentheses ..
(+24r^2-6r+32r-8)-90=0
We get rid of parentheses
24r^2-6r+32r-8-90=0
We add all the numbers together, and all the variables
24r^2+26r-98=0
a = 24; b = 26; c = -98;
Δ = b2-4ac
Δ = 262-4·24·(-98)
Δ = 10084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{10084}=\sqrt{4*2521}=\sqrt{4}*\sqrt{2521}=2\sqrt{2521}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{2521}}{2*24}=\frac{-26-2\sqrt{2521}}{48} $
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{2521}}{2*24}=\frac{-26+2\sqrt{2521}}{48} $

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