11(v-33)=3(v-33)8v

Solution for 11(v-33)=3(v-33)8v equation:

11(v-33)=3(v-33)8v

We move all terms to the left:

11(v-33)-(3(v-33)8v)=0

We multiply parentheses

11v-(3(v-33)8v)-363=0


We calculate terms in parentheses: -(3(v-33)8v), so:

3(v-33)8v

We multiply parentheses

24v^2-792v

Back to the equation:

-(24v^2-792v)


We get rid of parentheses

-24v^2+11v+792v-363=0

We add all the numbers together, and all the variables

-24v^2+803v-363=0

a = -24; b = 803; c = -363;
Δ = b2-4ac
Δ = 8032-4·(-24)·(-363)
Δ = 609961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{609961}=781$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(803)-781}{2*-24}=\frac{-1584}{-48}
=+33
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(803)+781}{2*-24}=\frac{-22}{-48}
=11/24
$