2x^2=3x-16x^2

Solution for 2x^2=3x-16x^2 equation:

2x^2=3x-16x^2

We move all terms to the left:

2x^2-(3x-16x^2)=0

We get rid of parentheses

2x^2+16x^2-3x=0

We add all the numbers together, and all the variables

18x^2-3x=0

a = 18; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·18·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*18}=\frac{0}{36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*18}=\frac{6}{36}
=1/6
$