4x2+78x+144=0

Solution for 4x2+78x+144=0 equation:

4x^2+78x+144=0

a = 4; b = 78; c = +144;
Δ = b2-4ac
Δ = 782-4·4·144
Δ = 3780
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:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-6\sqrt{105}}{2*4}=\frac{-78-6\sqrt{105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+6\sqrt{105}}{2*4}=\frac{-78+6\sqrt{105}}{8}
$