45=30+40x-16x^2

Solution for 45=30+40x-16x^2 equation:

45=30+40x-16x^2

We move all terms to the left:

45-(30+40x-16x^2)=0

We get rid of parentheses

16x^2-40x-30+45=0

We add all the numbers together, and all the variables

16x^2-40x+15=0

a = 16; b = -40; c = +15;
Δ = b2-4ac
Δ = -402-4·16·15
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{10}}{2*16}=\frac{40-8\sqrt{10}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{10}}{2*16}=\frac{40+8\sqrt{10}}{32}
$