Answer
The value of the discriminant of the given equation is $\sqrt{25}$, which is $>0$. Therefore, there are two unequal real solutions that will be obtained.
Work Step by Step
Simplify $10x(x + 4) = 15x - 15$:
$10x^2+40x=15x-15$
Add $15$ to both sides.
$10x^2+40x+15=15x-15+15$
$10x^2+40x+15=15x$
Subtract $15x$ from both sides.
$10x^2+40x+15-15x=15x-15x$
$10x^2+25x+15=0$
Compute for the discriminant.
$a=10$, $b=25$, $c=15$
$b^2-4ac = 25^2-(4⋅10⋅15)$
$b^2-4ac = \sqrt {25}$
Note that the discriminant tells the number and types of solution. If:
$b^2-4ac > 0$: Two unequal real solutions
$b^2-4ac = 0$: One solution (a repeated solution) that is
a real number
$b^2-4ac < 0$: No real solution; two imaginary solutions
The value of the discriminant of the given equation is $\sqrt{25}$, which is $>0$. Therefore, there are two unequal real solutions that will be obtained.
