-16x^2+60x+6=40

Solution for -16x^2+60x+6=40 equation:

-16x^2+60x+6=40

We move all terms to the left:

-16x^2+60x+6-(40)=0

We add all the numbers together, and all the variables

-16x^2+60x-34=0

a = -16; b = 60; c = -34;
Δ = b2-4ac
Δ = 602-4·(-16)·(-34)
Δ = 1424
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:

$\sqrt{\Delta}=\sqrt{1424}=\sqrt{16*89}=\sqrt{16}*\sqrt{89}=4\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{89}}{2*-16}=\frac{-60-4\sqrt{89}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{89}}{2*-16}=\frac{-60+4\sqrt{89}}{-32}
$