-2u+48=-5u(u-9)

Solution for -2u+48=-5u(u-9) equation:

-2u+48=-5u(u-9)

We move all terms to the left:

-2u+48-(-5u(u-9))=0


We calculate terms in parentheses: -(-5u(u-9)), so:

-5u(u-9)

We multiply parentheses

-5u^2+45u

Back to the equation:

-(-5u^2+45u)


We get rid of parentheses

5u^2-45u-2u+48=0

We add all the numbers together, and all the variables

5u^2-47u+48=0

a = 5; b = -47; c = +48;
Δ = b2-4ac
Δ = -472-4·5·48
Δ = 1249
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{-(-47)-\sqrt{1249}}{2*5}=\frac{47-\sqrt{1249}}{10}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{1249}}{2*5}=\frac{47+\sqrt{1249}}{10}
$