36x2-48x+14=0

Solution for 36x2-48x+14=0 equation:

36x^2-48x+14=0

a = 36; b = -48; c = +14;
Δ = b2-4ac
Δ = -482-4·36·14
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-12\sqrt{2}}{2*36}=\frac{48-12\sqrt{2}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+12\sqrt{2}}{2*36}=\frac{48+12\sqrt{2}}{72}
$