7v(2v-16)=5(v+4)

Solution for 7v(2v-16)=5(v+4) equation:

7v(2v-16)=5(v+4)

We move all terms to the left:

7v(2v-16)-(5(v+4))=0

We multiply parentheses

14v^2-112v-(5(v+4))=0


We calculate terms in parentheses: -(5(v+4)), so:

5(v+4)

We multiply parentheses

5v+20

Back to the equation:

-(5v+20)


We get rid of parentheses

14v^2-112v-5v-20=0

We add all the numbers together, and all the variables

14v^2-117v-20=0

a = 14; b = -117; c = -20;
Δ = b2-4ac
Δ = -1172-4·14·(-20)
Δ = 14809
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{-(-117)-\sqrt{14809}}{2*14}=\frac{117-\sqrt{14809}}{28}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-117)+\sqrt{14809}}{2*14}=\frac{117+\sqrt{14809}}{28}
$