144x^2+218x+21=0

Solution for 144x^2+218x+21=0 equation:

144x^2+218x+21=0

a = 144; b = 218; c = +21;
Δ = b2-4ac
Δ = 2182-4·144·21
Δ = 35428
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:

$\sqrt{\Delta}=\sqrt{35428}=\sqrt{4*8857}=\sqrt{4}*\sqrt{8857}=2\sqrt{8857}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(218)-2\sqrt{8857}}{2*144}=\frac{-218-2\sqrt{8857}}{288}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(218)+2\sqrt{8857}}{2*144}=\frac{-218+2\sqrt{8857}}{288}
$