45-56x+12x^2=0

Solution for 45-56x+12x^2=0 equation:

45-56x+12x^2=0

a = 12; b = -56; c = +45;
Δ = b2-4ac
Δ = -562-4·12·45
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{61}}{2*12}=\frac{56-4\sqrt{61}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{61}}{2*12}=\frac{56+4\sqrt{61}}{24}
$