14/2b^2-8=0

Solution for 14/2b^2-8=0 equation:

14/2b^2-8=0


Domain of the equation: 2b^2!=0

b^2!=0/2

b^2!=√0

b!=0

b∈R


We multiply all the terms by the denominator


-8*2b^2+14=0

Wy multiply elements

-16b^2+14=0

a = -16; b = 0; c = +14;
Δ = b2-4ac
Δ = 02-4·(-16)·14
Δ = 896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{14}}{2*-16}=\frac{0-8\sqrt{14}}{-32}
=-\frac{8\sqrt{14}}{-32}
=-\frac{\sqrt{14}}{-4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{14}}{2*-16}=\frac{0+8\sqrt{14}}{-32}
=\frac{8\sqrt{14}}{-32}
=\frac{\sqrt{14}}{-4}
$