63=2x+5x^2

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

63=2x+5x^2

We move all terms to the left:

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

We get rid of parentheses

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

a = -5; b = -2; c = +63;
Δ = b2-4ac
Δ = -22-4·(-5)·63
Δ = 1264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{79}}{2*-5}=\frac{2-4\sqrt{79}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{79}}{2*-5}=\frac{2+4\sqrt{79}}{-10}
$