30-13x-3x^2=0

Solution for 30-13x-3x^2=0 equation:

30-13x-3x^2=0

a = -3; b = -13; c = +30;
Δ = b2-4ac
Δ = -132-4·(-3)·30
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-23}{2*-3}=\frac{-10}{-6}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+23}{2*-3}=\frac{36}{-6}
=-6
$