11=1/2(9x2)

Solution for 11=1/2(9x2) equation:

11=1/2(9x^2)

We move all terms to the left:

11-(1/2(9x^2))=0


Domain of the equation: 29x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-1/29x^2+11=0

We multiply all the terms by the denominator


11*29x^2-1=0

Wy multiply elements

319x^2-1=0

a = 319; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·319·(-1)
Δ = 1276
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:

$\sqrt{\Delta}=\sqrt{1276}=\sqrt{4*319}=\sqrt{4}*\sqrt{319}=2\sqrt{319}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{319}}{2*319}=\frac{0-2\sqrt{319}}{638}
=-\frac{2\sqrt{319}}{638}
=-\frac{\sqrt{319}}{319}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{319}}{2*319}=\frac{0+2\sqrt{319}}{638}
=\frac{2\sqrt{319}}{638}
=\frac{\sqrt{319}}{319}
$