7x^2+78x+144=0

Solution for 7x^2+78x+144=0 equation:

7x^2+78x+144=0

a = 7; b = 78; c = +144;
Δ = b2-4ac
Δ = 782-4·7·144
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-6\sqrt{57}}{2*7}=\frac{-78-6\sqrt{57}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+6\sqrt{57}}{2*7}=\frac{-78+6\sqrt{57}}{14}
$