(x^2)/2+2x-21=0

Solution for (x^2)/2+2x-21=0 equation:

(x^2)/2+2x-21=0

We multiply all the terms by the denominator


x^2+2x*2-21*2=0

We add all the numbers together, and all the variables

x^2+2x*2-42=0

Wy multiply elements

x^2+4x-42=0

a = 1; b = 4; c = -42;
Δ = b2-4ac
Δ = 42-4·1·(-42)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{46}}{2*1}=\frac{-4-2\sqrt{46}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{46}}{2*1}=\frac{-4+2\sqrt{46}}{2}
$