30v+27/40v+36=0

Solution for 30v+27/40v+36=0 equation:

30v+27/40v+36=0


Domain of the equation: 40v!=0

v!=0/40

v!=0

v∈R


We multiply all the terms by the denominator


30v*40v+36*40v+27=0

Wy multiply elements

1200v^2+1440v+27=0

a = 1200; b = 1440; c = +27;
Δ = b2-4ac
Δ = 14402-4·1200·27
Δ = 1944000
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:

$\sqrt{\Delta}=\sqrt{1944000}=\sqrt{129600*15}=\sqrt{129600}*\sqrt{15}=360\sqrt{15}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1440)-360\sqrt{15}}{2*1200}=\frac{-1440-360\sqrt{15}}{2400}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1440)+360\sqrt{15}}{2*1200}=\frac{-1440+360\sqrt{15}}{2400}
$