x^2-8=14x/3

Solution for x^2-8=14x/3 equation:

x^2-8=14x/3

We move all terms to the left:

x^2-8-(14x/3)=0

We add all the numbers together, and all the variables

x^2-(+14x/3)-8=0

We get rid of parentheses

x^2-14x/3-8=0

We multiply all the terms by the denominator


x^2*3-14x-8*3=0

We add all the numbers together, and all the variables

x^2*3-14x-24=0

Wy multiply elements

3x^2-14x-24=0

a = 3; b = -14; c = -24;
Δ = b2-4ac
Δ = -142-4·3·(-24)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-22}{2*3}=\frac{-8}{6}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+22}{2*3}=\frac{36}{6}
=6
$