25=5+37x-16x^2

Solution for 25=5+37x-16x^2 equation:

25=5+37x-16x^2

We move all terms to the left:

25-(5+37x-16x^2)=0

We get rid of parentheses

16x^2-37x-5+25=0

We add all the numbers together, and all the variables

16x^2-37x+20=0

a = 16; b = -37; c = +20;
Δ = b2-4ac
Δ = -372-4·16·20
Δ = 89
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{-(-37)-\sqrt{89}}{2*16}=\frac{37-\sqrt{89}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{89}}{2*16}=\frac{37+\sqrt{89}}{32}
$