81-72x+12x^2=0

Solution for 81-72x+12x^2=0 equation:

81-72x+12x^2=0

a = 12; b = -72; c = +81;
Δ = b2-4ac
Δ = -722-4·12·81
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-36}{2*12}=\frac{36}{24}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+36}{2*12}=\frac{108}{24}
=4+1/2
$