3x^2-2(5+3)=21+2(11)/(3-1)

Solution for 3x^2-2(5+3)=21+2(11)/(3-1) equation:

3x^2-2(5+3)=21+2(11)/(3-1)

We move all terms to the left:

3x^2-2(5+3)-(21+2(11)/(3-1))=0

We add all the numbers together, and all the variables

3x^2-28-(21+211/2)=0

We get rid of parentheses

3x^2-28-21-211/2=0

We multiply all the terms by the denominator


3x^2*2-211-28*2-21*2=0

We add all the numbers together, and all the variables

3x^2*2-309=0

Wy multiply elements

6x^2-309=0

a = 6; b = 0; c = -309;
Δ = b2-4ac
Δ = 02-4·6·(-309)
Δ = 7416
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:

$\sqrt{\Delta}=\sqrt{7416}=\sqrt{36*206}=\sqrt{36}*\sqrt{206}=6\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{206}}{2*6}=\frac{0-6\sqrt{206}}{12}
=-\frac{6\sqrt{206}}{12}
=-\frac{\sqrt{206}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{206}}{2*6}=\frac{0+6\sqrt{206}}{12}
=\frac{6\sqrt{206}}{12}
=\frac{\sqrt{206}}{2}
$