7=-16x^2+30x+6

Solution for 7=-16x^2+30x+6 equation:

7=-16x^2+30x+6

We move all terms to the left:

7-(-16x^2+30x+6)=0

We get rid of parentheses

16x^2-30x-6+7=0

We add all the numbers together, and all the variables

16x^2-30x+1=0

a = 16; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·16·1
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{209}}{2*16}=\frac{30-2\sqrt{209}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{209}}{2*16}=\frac{30+2\sqrt{209}}{32}
$