14x^2+4x-(29/3)=0

Solution for 14x^2+4x-(29/3)=0 equation:

14x^2+4x-(29/3)=0

We add all the numbers together, and all the variables

14x^2+4x-(+29/3)=0

We get rid of parentheses

14x^2+4x-29/3=0

We multiply all the terms by the denominator


14x^2*3+4x*3-29=0

Wy multiply elements

42x^2+12x-29=0

a = 42; b = 12; c = -29;
Δ = b2-4ac
Δ = 122-4·42·(-29)
Δ = 5016
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:

$\sqrt{\Delta}=\sqrt{5016}=\sqrt{4*1254}=\sqrt{4}*\sqrt{1254}=2\sqrt{1254}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{1254}}{2*42}=\frac{-12-2\sqrt{1254}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{1254}}{2*42}=\frac{-12+2\sqrt{1254}}{84}
$