15-43x-6x^2=0

Solution for 15-43x-6x^2=0 equation:

15-43x-6x^2=0

a = -6; b = -43; c = +15;
Δ = b2-4ac
Δ = -432-4·(-6)·15
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-47}{2*-6}=\frac{-4}{-12}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+47}{2*-6}=\frac{90}{-12}
=-7+1/2
$