64=5x+6x^2

Solution for 64=5x+6x^2 equation:

64=5x+6x^2

We move all terms to the left:

64-(5x+6x^2)=0

We get rid of parentheses

-6x^2-5x+64=0

a = -6; b = -5; c = +64;
Δ = b2-4ac
Δ = -52-4·(-6)·64
Δ = 1561
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{1561}}{2*-6}=\frac{5-\sqrt{1561}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{1561}}{2*-6}=\frac{5+\sqrt{1561}}{-12}
$