35=105x-16x^2

Solution for 35=105x-16x^2 equation:

35=105x-16x^2

We move all terms to the left:

35-(105x-16x^2)=0

We get rid of parentheses

16x^2-105x+35=0

a = 16; b = -105; c = +35;
Δ = b2-4ac
Δ = -1052-4·16·35
Δ = 8785
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{-(-105)-\sqrt{8785}}{2*16}=\frac{105-\sqrt{8785}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{8785}}{2*16}=\frac{105+\sqrt{8785}}{32}
$