-16x^2+230x=350

Solution for -16x^2+230x=350 equation:

-16x^2+230x=350

We move all terms to the left:

-16x^2+230x-(350)=0

a = -16; b = 230; c = -350;
Δ = b2-4ac
Δ = 2302-4·(-16)·(-350)
Δ = 30500
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:

$\sqrt{\Delta}=\sqrt{30500}=\sqrt{100*305}=\sqrt{100}*\sqrt{305}=10\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(230)-10\sqrt{305}}{2*-16}=\frac{-230-10\sqrt{305}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(230)+10\sqrt{305}}{2*-16}=\frac{-230+10\sqrt{305}}{-32}
$