X^2+3x^2-14x-20=0

Solution for X^2+3x^2-14x-20=0 equation:

X^2+3X^2-14X-20=0

We add all the numbers together, and all the variables

4X^2-14X-20=0

a = 4; b = -14; c = -20;
Δ = b2-4ac
Δ = -142-4·4·(-20)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{129}}{2*4}=\frac{14-2\sqrt{129}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{129}}{2*4}=\frac{14+2\sqrt{129}}{8}
$