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: $ax^2+bx+c=0$
$(2x-5)^2=121$
$4x^2-20x+25=121$
$4x^2-20x+25-121=0$
$4x^2-20x-96=0$
In this equation $a=4$, $b=-20$ and $c=-96$.
$D= b^2-4ac= (-20)^2-4*4*(-96)=400+96*16=1936>0$
Therefore, this equation has 2 real solutions.
