-21=(-8u+5)(u-6)

Solution for -21=(-8u+5)(u-6) equation:

-21=(-8u+5)(u-6)

We move all terms to the left:

-21-((-8u+5)(u-6))=0

We multiply parentheses ..

-((-8u^2+48u+5u-30))-21=0


We calculate terms in parentheses: -((-8u^2+48u+5u-30)), so:

(-8u^2+48u+5u-30)

We get rid of parentheses

-8u^2+48u+5u-30

We add all the numbers together, and all the variables

-8u^2+53u-30

Back to the equation:

-(-8u^2+53u-30)


We get rid of parentheses

8u^2-53u+30-21=0

We add all the numbers together, and all the variables

8u^2-53u+9=0

a = 8; b = -53; c = +9;
Δ = b2-4ac
Δ = -532-4·8·9
Δ = 2521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-\sqrt{2521}}{2*8}=\frac{53-\sqrt{2521}}{16}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{2521}}{2*8}=\frac{53+\sqrt{2521}}{16}
$