30x+x^2=144

Solution for 30x+x^2=144 equation:

30x+x^2=144

We move all terms to the left:

30x+x^2-(144)=0

a = 1; b = 30; c = -144;
Δ = b2-4ac
Δ = 302-4·1·(-144)
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{41}}{2*1}=\frac{-30-6\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{41}}{2*1}=\frac{-30+6\sqrt{41}}{2}
$