16x^2+32x=30x^2-50x

Solution for 16x^2+32x=30x^2-50x equation:

16x^2+32x=30x^2-50x

We move all terms to the left:

16x^2+32x-(30x^2-50x)=0

We get rid of parentheses

16x^2-30x^2+32x+50x=0

We add all the numbers together, and all the variables

-14x^2+82x=0

a = -14; b = 82; c = 0;
Δ = b2-4ac
Δ = 822-4·(-14)·0
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-82}{2*-14}=\frac{-164}{-28}
=5+6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+82}{2*-14}=\frac{0}{-28}
=0
$