6+5a-6a^2=0

Solution for 6+5a-6a^2=0 equation:

6+5a-6a^2=0

a = -6; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·(-6)·6
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-13}{2*-6}=\frac{-18}{-12}
=1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+13}{2*-6}=\frac{8}{-12}
=-2/3
$