6u+38=8u(u+5)

Solution for 6u+38=8u(u+5) equation:

6u+38=8u(u+5)

We move all terms to the left:

6u+38-(8u(u+5))=0


We calculate terms in parentheses: -(8u(u+5)), so:

8u(u+5)

We multiply parentheses

8u^2+40u

Back to the equation:

-(8u^2+40u)


We get rid of parentheses

-8u^2+6u-40u+38=0

We add all the numbers together, and all the variables

-8u^2-34u+38=0

a = -8; b = -34; c = +38;
Δ = b2-4ac
Δ = -342-4·(-8)·38
Δ = 2372
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2372}=\sqrt{4*593}=\sqrt{4}*\sqrt{593}=2\sqrt{593}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{593}}{2*-8}=\frac{34-2\sqrt{593}}{-16}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{593}}{2*-8}=\frac{34+2\sqrt{593}}{-16}
$