5x+4x^2=82.

Solution for 5x+4x^2=82. equation:

5x+4x^2=82.

We move all terms to the left:

5x+4x^2-(82.)=0

We add all the numbers together, and all the variables

4x^2+5x-82=0

a = 4; b = 5; c = -82;
Δ = b2-4ac
Δ = 52-4·4·(-82)
Δ = 1337
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{1337}}{2*4}=\frac{-5-\sqrt{1337}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{1337}}{2*4}=\frac{-5+\sqrt{1337}}{8}
$