166x^2=-2x^2+152x-32

Solution for 166x^2=-2x^2+152x-32 equation:

166x^2=-2x^2+152x-32

We move all terms to the left:

166x^2-(-2x^2+152x-32)=0

We get rid of parentheses

166x^2+2x^2-152x+32=0

We add all the numbers together, and all the variables

168x^2-152x+32=0

a = 168; b = -152; c = +32;
Δ = b2-4ac
Δ = -1522-4·168·32
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-152)-40}{2*168}=\frac{112}{336}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-152)+40}{2*168}=\frac{192}{336}
=4/7
$