6x^2-14x-96=16/3

Solution for 6x^2-14x-96=16/3 equation:

6x^2-14x-96=16/3

We move all terms to the left:

6x^2-14x-96-(16/3)=0

We add all the numbers together, and all the variables

6x^2-14x-96-(+16/3)=0

We get rid of parentheses

6x^2-14x-96-16/3=0

We multiply all the terms by the denominator


6x^2*3-14x*3-16-96*3=0

We add all the numbers together, and all the variables

6x^2*3-14x*3-304=0

Wy multiply elements

18x^2-42x-304=0

a = 18; b = -42; c = -304;
Δ = b2-4ac
Δ = -422-4·18·(-304)
Δ = 23652
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:

$\sqrt{\Delta}=\sqrt{23652}=\sqrt{324*73}=\sqrt{324}*\sqrt{73}=18\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-18\sqrt{73}}{2*18}=\frac{42-18\sqrt{73}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+18\sqrt{73}}{2*18}=\frac{42+18\sqrt{73}}{36}
$