5x(1/2)2+x(2)=46

Solution for 5x(1/2)2+x(2)=46 equation:

5x(1/2)2+x(2)=46

We move all terms to the left:

5x(1/2)2+x(2)-(46)=0

We add all the numbers together, and all the variables

5x(+1/2)2+x2-46=0

We add all the numbers together, and all the variables

x^2+5x(+1/2)2-46=0

We multiply parentheses

x^2+10x^2-46=0

We add all the numbers together, and all the variables

11x^2-46=0

a = 11; b = 0; c = -46;
Δ = b2-4ac
Δ = 02-4·11·(-46)
Δ = 2024
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:

$\sqrt{\Delta}=\sqrt{2024}=\sqrt{4*506}=\sqrt{4}*\sqrt{506}=2\sqrt{506}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{506}}{2*11}=\frac{0-2\sqrt{506}}{22}
=-\frac{2\sqrt{506}}{22}
=-\frac{\sqrt{506}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{506}}{2*11}=\frac{0+2\sqrt{506}}{22}
=\frac{2\sqrt{506}}{22}
=\frac{\sqrt{506}}{11}
$