Question

Solve the equation 6w2 – 7w – 20 = 0.

A. w = –4⁄3, w = 2⁄5
B. w = –4⁄3, w = 5⁄2
C. w = –3⁄4, w = 5⁄2
D. w = –5⁄2, w = 4⁄3

Answer 1

`\large\boxed{B.\ w=-(4)/(3),\ w=(5)/(2)}`

Explanation:

`6w^2-7w-20=0\\\\6w^2-15w+8w-20=0\\\\3w(2w-5)+4(2w-5)=0\\\\(2w-5)(3w+4)=0\iff2w-5=0\ \vee\ 3w+4=0\\\\2w-5=0\qquad\text{add 5 to both sides}\\2w=5\qquad\text{divide both sides by 2}\\\boxed{w=(5)/(2)}\\\\3w+4=0\qquad\text{subtract 4 from both sides}\\3w=-4\qquad\text{divide both sides by 3}\\\boxed{w=-(4)/(3)}`