V(x)=(10-2x)(8-2x)

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Solution for V(x)=(10-2x)(8-2x) equation:



(V)=(10-2V)(8-2V)
We move all terms to the left:
(V)-((10-2V)(8-2V))=0
We add all the numbers together, and all the variables
V-((-2V+10)(-2V+8))=0
We multiply parentheses ..
-((+4V^2-16V-20V+80))+V=0
We calculate terms in parentheses: -((+4V^2-16V-20V+80)), so:
(+4V^2-16V-20V+80)
We get rid of parentheses
4V^2-16V-20V+80
We add all the numbers together, and all the variables
4V^2-36V+80
Back to the equation:
-(4V^2-36V+80)
We add all the numbers together, and all the variables
V-(4V^2-36V+80)=0
We get rid of parentheses
-4V^2+V+36V-80=0
We add all the numbers together, and all the variables
-4V^2+37V-80=0
a = -4; b = 37; c = -80;
Δ = b2-4ac
Δ = 372-4·(-4)·(-80)
Δ = 89
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{-(37)-\sqrt{89}}{2*-4}=\frac{-37-\sqrt{89}}{-8} $
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{89}}{2*-4}=\frac{-37+\sqrt{89}}{-8} $

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