3r(4r-1)+5=26

Solution for 3r(4r-1)+5=26 equation:

3r(4r-1)+5=26

We move all terms to the left:

3r(4r-1)+5-(26)=0

We add all the numbers together, and all the variables

3r(4r-1)-21=0

We multiply parentheses

12r^2-3r-21=0

a = 12; b = -3; c = -21;
Δ = b2-4ac
Δ = -32-4·12·(-21)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{113}}{2*12}=\frac{3-3\sqrt{113}}{24}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{113}}{2*12}=\frac{3+3\sqrt{113}}{24}
$