5x^2=84+x

Solution for 5x^2=84+x equation:

5x^2=84+x

We move all terms to the left:

5x^2-(84+x)=0

We add all the numbers together, and all the variables

5x^2-(x+84)=0

We get rid of parentheses

5x^2-x-84=0

We add all the numbers together, and all the variables

5x^2-1x-84=0

a = 5; b = -1; c = -84;
Δ = b2-4ac
Δ = -12-4·5·(-84)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-41}{2*5}=\frac{-40}{10}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+41}{2*5}=\frac{42}{10}
=4+1/5
$