0.5(1-4.1v)=-7.3(v+6.2)1.9v

Solution for 0.5(1-4.1v)=-7.3(v+6.2)1.9v equation:

0.5(1-4.1v)=-7.3(v+6.2)1.9v

We move all terms to the left:

0.5(1-4.1v)-(-7.3(v+6.2)1.9v)=0

We add all the numbers together, and all the variables

0.5(-4.1v+1)-(-7.3(v+6.2)1.9v)=0

We multiply parentheses

-2v-(-7.3(v+6.2)1.9v)+0.5=0


We calculate terms in parentheses: -(-7.3(v+6.2)1.9v), so:

-7.3(v+6.2)1.9v

We multiply parentheses

-7v^2-43.4v

Back to the equation:

-(-7v^2-43.4v)


We get rid of parentheses

7v^2+43.4v-2v+0.5=0

We add all the numbers together, and all the variables

7v^2+41.4v+0.5=0

a = 7; b = 41.4; c = +0.5;
Δ = b2-4ac
Δ = 41.42-4·7·0.5
Δ = 1699.96
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{-(41.4)-\sqrt{1699.96}}{2*7}=\frac{-41.4-\sqrt{1699.96}}{14}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41.4)+\sqrt{1699.96}}{2*7}=\frac{-41.4+\sqrt{1699.96}}{14}
$