## Precalculus (6th Edition)

$4x^{2}=-6x+3$ Take all terms to the left side: $4x^{2}+6x-3=0$ The discriminant is given by $b^{2}-4ac$. For this equation, $a=4$, $b=6$ and $c=-3$ Let the discriminant be $D$. Substitute the known values into the formula and evaluate: $D=6^{2}-4(4)(-3)=36+48=84$ Since the discriminant is equal to a positive, non-perfect square number, the equation has two solutions and they are irrational numbers.