225x^2-150x+25=33

Solution for 225x^2-150x+25=33 equation:

225x^2-150x+25=33

We move all terms to the left:

225x^2-150x+25-(33)=0

We add all the numbers together, and all the variables

225x^2-150x-8=0

a = 225; b = -150; c = -8;
Δ = b2-4ac
Δ = -1502-4·225·(-8)
Δ = 29700
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:

$\sqrt{\Delta}=\sqrt{29700}=\sqrt{900*33}=\sqrt{900}*\sqrt{33}=30\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-30\sqrt{33}}{2*225}=\frac{150-30\sqrt{33}}{450}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+30\sqrt{33}}{2*225}=\frac{150+30\sqrt{33}}{450}
$