9-0.2v(v-8)=0.3(6v-8)

Solution for 9-0.2v(v-8)=0.3(6v-8) equation:

9-0.2v(v-8)=0.3(6v-8)

We move all terms to the left:

9-0.2v(v-8)-(0.3(6v-8))=0

We multiply parentheses

-0v^2-0v-(0.3(6v-8))+9=0


We calculate terms in parentheses: -(0.3(6v-8)), so:

0.3(6v-8)

We multiply parentheses

1.8v-2.4

Back to the equation:

-(1.8v-2.4)


We add all the numbers together, and all the variables

-1v^2-1v-(1.8v-2.4)+9=0

We get rid of parentheses

-1v^2-1v-1.8v+2.4+9=0

We add all the numbers together, and all the variables

-1v^2-2.8v+11.4=0

a = -1; b = -2.8; c = +11.4;
Δ = b2-4ac
Δ = -2.82-4·(-1)·11.4
Δ = 53.44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2.8)-\sqrt{53.44}}{2*-1}=\frac{2.8-\sqrt{53.44}}{-2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.8)+\sqrt{53.44}}{2*-1}=\frac{2.8+\sqrt{53.44}}{-2}
$