Answer
2 real solutions.
Work Step by Step
To find the number of solutions in a quadratic formula, we need to find the determinant. The determinant follows these rules:
If D<0: no real solutions
If D=0: 1 real solution
If D>0: 2 real solutions
The determinant is generally calculated by this formula: $ D={b^2-4ac}$.
The general formula for quadratic equations is: $ax^2+bx+c=0$
$6x^2+5x-2=-3$
$6x^2+5x-2+3=0$
$6x^2+5x+1=0$
In this equation, $a=6$, $b=5$ and $c=1$.
$D= b^2-4ac= 5^2-4*6*1=25-24=1>0$
Therefore, this equation has 2 real solutions.
