4v^2-7v-3=0

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Solution for 4v^2-7v-3=0 equation: 



4v^2-7v-3=0

a = 4; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·4·(-3)
Δ = 97
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{-(-7)-\sqrt{97}}{2*4}=\frac{7-\sqrt{97}}{8}
$


$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{97}}{2*4}=\frac{7+\sqrt{97}}{8}
$

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