x^2+3x-1954=0

Solution for x^2+3x-1954=0 equation:

x^2+3x-1954=0

a = 1; b = 3; c = -1954;
Δ = b2-4ac
Δ = 32-4·1·(-1954)
Δ = 7825
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:

$\sqrt{\Delta}=\sqrt{7825}=\sqrt{25*313}=\sqrt{25}*\sqrt{313}=5\sqrt{313}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5\sqrt{313}}{2*1}=\frac{-3-5\sqrt{313}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5\sqrt{313}}{2*1}=\frac{-3+5\sqrt{313}}{2}
$