-x2+29x+342=0

Solution for -x2+29x+342=0 equation:

-x2+29x+342=0

We add all the numbers together, and all the variables

-1x^2+29x+342=0

a = -1; b = 29; c = +342;
Δ = b2-4ac
Δ = 292-4·(-1)·342
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-47}{2*-1}=\frac{-76}{-2}
=+38
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+47}{2*-1}=\frac{18}{-2}
=-9
$