21/2x2+10=31

Solution for 21/2x2+10=31 equation:

21/2x^2+10=31

We move all terms to the left:

21/2x^2+10-(31)=0


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

x^2!=0/2

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

21/2x^2-21=0

We multiply all the terms by the denominator


-21*2x^2+21=0

Wy multiply elements

-42x^2+21=0

a = -42; b = 0; c = +21;
Δ = b2-4ac
Δ = 02-4·(-42)·21
Δ = 3528
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:

$\sqrt{\Delta}=\sqrt{3528}=\sqrt{1764*2}=\sqrt{1764}*\sqrt{2}=42\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-42\sqrt{2}}{2*-42}=\frac{0-42\sqrt{2}}{-84}
=-\frac{42\sqrt{2}}{-84}
=-\frac{\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+42\sqrt{2}}{2*-42}=\frac{0+42\sqrt{2}}{-84}
=\frac{42\sqrt{2}}{-84}
=\frac{\sqrt{2}}{-2}
$