8x-3-x^2=0

Solution for 8x-3-x^2=0 equation:

8x-3-x^2=0

We add all the numbers together, and all the variables

-1x^2+8x-3=0

a = -1; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·(-1)·(-3)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{13}}{2*-1}=\frac{-8-2\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{13}}{2*-1}=\frac{-8+2\sqrt{13}}{-2}
$