7x^2-180x+450=0

Solution for 7x^2-180x+450=0 equation:

7x^2-180x+450=0

a = 7; b = -180; c = +450;
Δ = b2-4ac
Δ = -1802-4·7·450
Δ = 19800
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:

$\sqrt{\Delta}=\sqrt{19800}=\sqrt{900*22}=\sqrt{900}*\sqrt{22}=30\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-30\sqrt{22}}{2*7}=\frac{180-30\sqrt{22}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+30\sqrt{22}}{2*7}=\frac{180+30\sqrt{22}}{14}
$