3x2=2x+13/3

Solution for 3x2=2x+13/3 equation:

3x^2=2x+13/3

We move all terms to the left:

3x^2-(2x+13/3)=0

We add all the numbers together, and all the variables

3x^2-(+2x+13/3)=0

We get rid of parentheses

3x^2-2x-13/3=0

We multiply all the terms by the denominator


3x^2*3-2x*3-13=0

Wy multiply elements

9x^2-6x-13=0

a = 9; b = -6; c = -13;
Δ = b2-4ac
Δ = -62-4·9·(-13)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{14}}{2*9}=\frac{6-6\sqrt{14}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{14}}{2*9}=\frac{6+6\sqrt{14}}{18}
$