7.5=4+35x-16x^2

Solution for 7.5=4+35x-16x^2 equation:

7.5=4+35x-16x^2

We move all terms to the left:

7.5-(4+35x-16x^2)=0

We get rid of parentheses

16x^2-35x-4+7.5=0

We add all the numbers together, and all the variables

16x^2-35x+3.5=0

a = 16; b = -35; c = +3.5;
Δ = b2-4ac
Δ = -352-4·16·3.5
Δ = 1001
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{-(-35)-\sqrt{1001}}{2*16}=\frac{35-\sqrt{1001}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1001}}{2*16}=\frac{35+\sqrt{1001}}{32}
$