Question

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth 5y^2-8y=2

Answer 1

Answer:

Step-by-step explanation:

First, rewrite the equation (all terms should be in the left side):

$5y^2-8y-2=0.$

In this equation,

• $a=5;$
• $b=-8;$
• $c=-2.$

Then the discriminant

$D=b^2 -4ac=(-8)^2-4\cdot 5\cdot (-2)=64+40=104.$

Then

$y_1=\dfrac{-b+\sqrt{D}}{2a}=\dfrac{-(-8)+\sqrt{104}}{2\cdot 5}=\dfrac{8+2\sqrt{26}}{10}=\dfrac{4+\sqrt{26}}{5},\\ \\y_2=\dfrac{-b-\sqrt{D}}{2a}=\dfrac{-(-8)-\sqrt{104}}{2\cdot 5}=\dfrac{8-2\sqrt{26}}{10}=\dfrac{4-\sqrt{26}}{5}.$