3x^2+30x=16

Solution for 3x^2+30x=16 equation:

3x^2+30x=16

We move all terms to the left:

3x^2+30x-(16)=0

a = 3; b = 30; c = -16;
Δ = b2-4ac
Δ = 302-4·3·(-16)
Δ = 1092
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:

$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{273}}{2*3}=\frac{-30-2\sqrt{273}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{273}}{2*3}=\frac{-30+2\sqrt{273}}{6}
$