5x2=53x+84

Solution for 5x2=53x+84 equation:

5x^2=53x+84

We move all terms to the left:

5x^2-(53x+84)=0

We get rid of parentheses

5x^2-53x-84=0

a = 5; b = -53; c = -84;
Δ = b2-4ac
Δ = -532-4·5·(-84)
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-67}{2*5}=\frac{-14}{10}
=-1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+67}{2*5}=\frac{120}{10}
=12
$