2(x)2+2/5=19

Solution for 2(x)2+2/5=19 equation:

2(x)2+2/5=19

We move all terms to the left:

2(x)2+2/5-(19)=0

determiningTheFunctionDomain
2x2-19+2/5=0

We add all the numbers together, and all the variables

2x^2-19+2/5=0

We multiply all the terms by the denominator


2x^2*5+2-19*5=0

We add all the numbers together, and all the variables

2x^2*5-93=0

Wy multiply elements

10x^2-93=0

a = 10; b = 0; c = -93;
Δ = b2-4ac
Δ = 02-4·10·(-93)
Δ = 3720
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:

$\sqrt{\Delta}=\sqrt{3720}=\sqrt{4*930}=\sqrt{4}*\sqrt{930}=2\sqrt{930}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{930}}{2*10}=\frac{0-2\sqrt{930}}{20}
=-\frac{2\sqrt{930}}{20}
=-\frac{\sqrt{930}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{930}}{2*10}=\frac{0+2\sqrt{930}}{20}
=\frac{2\sqrt{930}}{20}
=\frac{\sqrt{930}}{10}
$