Answer:
x=-3 or x=3/2
Step-by-step explanation:
We are given the following equation:
2x^2+5x-9=2x
We are asked to find the roots. That means just solve it for x.
2x^2+5x-9=2x
Subtract 2x on both sides:
2x^2+3x-9=0
Let's see if we can put this in factored form.
Compare
2x^2+3x-9=0
and
ax^2+bx+c=0.
a=2, b=3 , c=-9
We have to find two numbers that multiply to be ac and add up to be b.
ac=-18
b=3
What are two numbers that multiply to be -18 and add to be 3?
Say -3 and 6.
So we are going to factor 2x^2-3x+6x-9=0
The first two terms have a common factor of x.
The last two terms have a common factor of 3.
2x^2-3x+6x-9=0
x(2x-3)+3(2x-3)=0
Now we can factor the (x-3) out of those 2 terms there since they share that common factor:
(x+3)(2x-3)=0
(x+3)(2x-3)=0 implies x+3=0 or 2x-3=0.
So we must solve x+3=0 and 2x-3=0
x+3=0
Subtract 3 on both sides:
x=-3
2x-3=0
Add 3 on both sides:
2x=3
Divide both sides by 2:
x=3/2
The solutions are x=3 or x=-3/2
