5x^2+106x+144=0

Solution for 5x^2+106x+144=0 equation:

5x^2+106x+144=0

a = 5; b = 106; c = +144;
Δ = b2-4ac
Δ = 1062-4·5·144
Δ = 8356
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:

$\sqrt{\Delta}=\sqrt{8356}=\sqrt{4*2089}=\sqrt{4}*\sqrt{2089}=2\sqrt{2089}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(106)-2\sqrt{2089}}{2*5}=\frac{-106-2\sqrt{2089}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(106)+2\sqrt{2089}}{2*5}=\frac{-106+2\sqrt{2089}}{10}
$