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

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}
$