144=4x^2+84x

Solution for 144=4x^2+84x equation:

144=4x^2+84x

We move all terms to the left:

144-(4x^2+84x)=0

We get rid of parentheses

-4x^2-84x+144=0

a = -4; b = -84; c = +144;
Δ = b2-4ac
Δ = -842-4·(-4)·144
Δ = 9360
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:

$\sqrt{\Delta}=\sqrt{9360}=\sqrt{144*65}=\sqrt{144}*\sqrt{65}=12\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-12\sqrt{65}}{2*-4}=\frac{84-12\sqrt{65}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+12\sqrt{65}}{2*-4}=\frac{84+12\sqrt{65}}{-8}
$