345+8x-x^2=0

Solution for 345+8x-x^2=0 equation:

345+8x-x^2=0

We add all the numbers together, and all the variables

-1x^2+8x+345=0

a = -1; b = 8; c = +345;
Δ = b2-4ac
Δ = 82-4·(-1)·345
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-38}{2*-1}=\frac{-46}{-2}
=+23
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+38}{2*-1}=\frac{30}{-2}
=-15
$