3x^2=-x+14

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

3x^2=-x+14

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x^2-(-1x+14)=0

We get rid of parentheses

3x^2+1x-14=0

We add all the numbers together, and all the variables

3x^2+x-14=0

a = 3; b = 1; c = -14;
Δ = b2-4ac
Δ = 12-4·3·(-14)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-13}{2*3}=\frac{-14}{6}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+13}{2*3}=\frac{12}{6}
=2
$