7x^2+144x+576=0

Solution for 7x^2+144x+576=0 equation:

7x^2+144x+576=0

a = 7; b = 144; c = +576;
Δ = b2-4ac
Δ = 1442-4·7·576
Δ = 4608
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:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-48\sqrt{2}}{2*7}=\frac{-144-48\sqrt{2}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+48\sqrt{2}}{2*7}=\frac{-144+48\sqrt{2}}{14}
$