3x^2=x+80

Solution for 3x^2=x+80 equation:

3x^2=x+80

We move all terms to the left:

3x^2-(x+80)=0

We get rid of parentheses

3x^2-x-80=0

We add all the numbers together, and all the variables

3x^2-1x-80=0

a = 3; b = -1; c = -80;
Δ = b2-4ac
Δ = -12-4·3·(-80)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-31}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+31}{2*3}=\frac{32}{6}
=5+1/3
$