## Algebra 1: Common Core (15th Edition)

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.