2x2-3x-34=4/3

Solution for 2x2-3x-34=4/3 equation:

2x^2-3x-34=4/3

We move all terms to the left:

2x^2-3x-34-(4/3)=0

We add all the numbers together, and all the variables

2x^2-3x-34-(+4/3)=0

We get rid of parentheses

2x^2-3x-34-4/3=0

We multiply all the terms by the denominator


2x^2*3-3x*3-4-34*3=0

We add all the numbers together, and all the variables

2x^2*3-3x*3-106=0

Wy multiply elements

6x^2-9x-106=0

a = 6; b = -9; c = -106;
Δ = b2-4ac
Δ = -92-4·6·(-106)
Δ = 2625
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:

$\sqrt{\Delta}=\sqrt{2625}=\sqrt{25*105}=\sqrt{25}*\sqrt{105}=5\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-5\sqrt{105}}{2*6}=\frac{9-5\sqrt{105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+5\sqrt{105}}{2*6}=\frac{9+5\sqrt{105}}{12}
$