11x^2+6x+(1/2)=0

Solution for 11x^2+6x+(1/2)=0 equation:

11x^2+6x+(1/2)=0

We add all the numbers together, and all the variables

11x^2+6x+(+1/2)=0

We get rid of parentheses

11x^2+6x+1/2=0

We multiply all the terms by the denominator


11x^2*2+6x*2+1=0

Wy multiply elements

22x^2+12x+1=0

a = 22; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·22·1
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{14}}{2*22}=\frac{-12-2\sqrt{14}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{14}}{2*22}=\frac{-12+2\sqrt{14}}{44}
$