92=4(2r-5)r=

Solution for 92=4(2r-5)r= equation:

92=4(2r-5)r=

We move all terms to the left:

92-(4(2r-5)r)=0


We calculate terms in parentheses: -(4(2r-5)r), so:

4(2r-5)r

We multiply parentheses

8r^2-20r

Back to the equation:

-(8r^2-20r)


We get rid of parentheses

-8r^2+20r+92=0

a = -8; b = 20; c = +92;
Δ = b2-4ac
Δ = 202-4·(-8)·92
Δ = 3344
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:

$\sqrt{\Delta}=\sqrt{3344}=\sqrt{16*209}=\sqrt{16}*\sqrt{209}=4\sqrt{209}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{209}}{2*-8}=\frac{-20-4\sqrt{209}}{-16}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{209}}{2*-8}=\frac{-20+4\sqrt{209}}{-16}
$