63=5x+2x^2

Solution for 63=5x+2x^2 equation:

63=5x+2x^2

We move all terms to the left:

63-(5x+2x^2)=0

We get rid of parentheses

-2x^2-5x+63=0

a = -2; b = -5; c = +63;
Δ = b2-4ac
Δ = -52-4·(-2)·63
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-23}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+23}{2*-2}=\frac{28}{-4}
=-7
$