x*x+100x-291=0

Solution for x*x+100x-291=0 equation:

x*x+100x-291=0

We add all the numbers together, and all the variables

100x+x*x-291=0

Wy multiply elements

x^2+100x-291=0

a = 1; b = 100; c = -291;
Δ = b2-4ac
Δ = 1002-4·1·(-291)
Δ = 11164
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:

$\sqrt{\Delta}=\sqrt{11164}=\sqrt{4*2791}=\sqrt{4}*\sqrt{2791}=2\sqrt{2791}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-2\sqrt{2791}}{2*1}=\frac{-100-2\sqrt{2791}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+2\sqrt{2791}}{2*1}=\frac{-100+2\sqrt{2791}}{2}
$