30x+16=-7x^2

Solution for 30x+16=-7x^2 equation:

30x+16=-7x^2

We move all terms to the left:

30x+16-(-7x^2)=0

We get rid of parentheses

7x^2+30x+16=0

a = 7; b = 30; c = +16;
Δ = b2-4ac
Δ = 302-4·7·16
Δ = 452
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:

$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{113}}{2*7}=\frac{-30-2\sqrt{113}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{113}}{2*7}=\frac{-30+2\sqrt{113}}{14}
$