8x-2x*x+7.5=0

Solution for 8x-2x*x+7.5=0 equation:

8x-2x*x+7.5=0

Wy multiply elements

-2x^2+8x+7.5=0

a = -2; b = 8; c = +7.5;
Δ = b2-4ac
Δ = 82-4·(-2)·7.5
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{31}}{2*-2}=\frac{-8-2\sqrt{31}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{31}}{2*-2}=\frac{-8+2\sqrt{31}}{-4}
$