x^2+14x/3-4/3=0

Solution for x^2+14x/3-4/3=0 equation:

x^2+14x/3-4/3=0

We multiply all the terms by the denominator


x^2*3+14x-4=0

Wy multiply elements

3x^2+14x-4=0

a = 3; b = 14; c = -4;
Δ = b2-4ac
Δ = 142-4·3·(-4)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{61}}{2*3}=\frac{-14-2\sqrt{61}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{61}}{2*3}=\frac{-14+2\sqrt{61}}{6}
$