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3000=0.042v^2
We move all terms to the left:
3000-(0.042v^2)=0
We get rid of parentheses
-0.042v^2+3000=0
a = -0.042; b = 0; c = +3000;
Δ = b2-4ac
Δ = 02-4·(-0.042)·3000
Δ = 504
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}$$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{504}=\sqrt{4*126}=\sqrt{4}*\sqrt{126}=2\sqrt{126}$$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{126}}{2*-0.042}=\frac{0-2\sqrt{126}}{-0.084} =-\frac{2\sqrt{126}}{-0.084} =-\frac{\sqrt{126}}{-0.042} $$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{126}}{2*-0.042}=\frac{0+2\sqrt{126}}{-0.084} =\frac{2\sqrt{126}}{-0.084} =\frac{\sqrt{126}}{-0.042} $
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