Question

find the discriminant.
3v² - 3 = 6v
what type of solutions does the equation have?
one real solution
two real solutions
two complex (non - real) solutions

Explanation:

Step1: Rewrite equation in standard form

First, rewrite $3v^{2}-3 = 6v$ as $3v^{2}-6v - 3=0$. For a quadratic equation $ax^{2}+bx + c = 0$, here $a = 3$, $b=-6$, $c=-3$.

Step2: Calculate the discriminant

The discriminant formula is $\Delta=b^{2}-4ac$. Substitute $a = 3$, $b=-6$, $c=-3$ into the formula: $\Delta=(-6)^{2}-4\times3\times(-3)=36 + 36=72$.

Step3: Determine the type of solutions

Since $\Delta=72>0$, the quadratic equation has two real solutions.

Answer:

Discriminant: 72
Type of solutions: two real solutions