Question

Solve 2x2 – 5x 1 = 3 for x.

Answer 1

2x^2-5x+1=3
2x^2= a -5x=b 1=c
the rule is: ax^2+bx+c= 0
therefore, we have to make the equation equals to zero:
2x^2-5x+1-3=0
2x^2-5x-2= 0
the rule here is: b^2-ac:
delta= 25-16=9
then you square the delta:
=√delta= 3
there are two ways to get x, either:
(-b-delta)÷2a
x...(1)= (5-3)÷4= 1/2
or, (b+delta)÷2a
x...(2)= (5+3)÷4= 2
hope it makes sense.

Answer 2

For this case we have the following polynomial:

$2x^2 - 5x + 1 = 3$

Rewriting the polynomial we have:

$2x^2 - 5x + 1 - 3 = 0\\2x^2 - 5x - 2 = 0$

Using the quadratic formula to find the solutions we have:

$x = \frac{-b+/-\sqrt{b^2 - 4ac}}{2a}$

Substituting values:

$x = \frac{-(-5)+/-\sqrt{(-5)^2 - 4(2)(-2)}}{2(2)}$

Rewriting:

$x = \frac{5+/-\sqrt{25+16}}{4}$

$x = \frac{5+/-\sqrt{41}}{4}$

Solution 1:

$x = \frac{5+\sqrt{41}}{4}$

Solution 2:

$x = \frac{5-\sqrt{41}}{4}$