4x^2+12x=144

Solution for 4x^2+12x=144 equation:

4x^2+12x=144

We move all terms to the left:

4x^2+12x-(144)=0

a = 4; b = 12; c = -144;
Δ = b2-4ac
Δ = 122-4·4·(-144)
Δ = 2448
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:

$\sqrt{\Delta}=\sqrt{2448}=\sqrt{144*17}=\sqrt{144}*\sqrt{17}=12\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{17}}{2*4}=\frac{-12-12\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{17}}{2*4}=\frac{-12+12\sqrt{17}}{8}
$