X2+3x-144=0

Solution for X2+3x-144=0 equation:

X2+3X-144=0

We add all the numbers together, and all the variables

X^2+3X-144=0

a = 1; b = 3; c = -144;
Δ = b2-4ac
Δ = 32-4·1·(-144)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{65}}{2*1}=\frac{-3-3\sqrt{65}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{65}}{2*1}=\frac{-3+3\sqrt{65}}{2}
$