2x2+45x+72=0

Solution for 2x2+45x+72=0 equation:

2x^2+45x+72=0

a = 2; b = 45; c = +72;
Δ = b2-4ac
Δ = 452-4·2·72
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{161}}{2*2}=\frac{-45-3\sqrt{161}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{161}}{2*2}=\frac{-45+3\sqrt{161}}{4}
$