2x^2+14x+47/2=0

Solution for 2x^2+14x+47/2=0 equation:

2x^2+14x+47/2=0

We multiply all the terms by the denominator


2x^2*2+14x*2+47=0

Wy multiply elements

4x^2+28x+47=0

a = 4; b = 28; c = +47;
Δ = b2-4ac
Δ = 282-4·4·47
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{2}}{2*4}=\frac{-28-4\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{2}}{2*4}=\frac{-28+4\sqrt{2}}{8}
$