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

determiningTheFunctionDomain
-7x^2+30x+16=0

a = -7; b = 30; c = +16;
Δ = b2-4ac
Δ = 302-4·(-7)·16
Δ = 1348
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:

$\sqrt{\Delta}=\sqrt{1348}=\sqrt{4*337}=\sqrt{4}*\sqrt{337}=2\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{337}}{2*-7}=\frac{-30-2\sqrt{337}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{337}}{2*-7}=\frac{-30+2\sqrt{337}}{-14}
$