Solve the equation for all real solution 4y^2+19y+17=0

y=-1.20 or - 3.56

Step-by-step explanation:

4y^2+19y+17=0

subtract 7 from both sides to have

4y^2+19y=-17

Divide through by 4

y^2+19/4 y=-17/4

Complete the square of LHS to obtain

(y+19/8) ^2 - (19/8) ^2=-17/4

simplifying further we have

(y+19/8) ^2=-17/4 + (19) ^2 / (8) ^2 = -17/4+361/64=-272+361/64=89/64

i. e. (y+19/8) ^2=89/64

taking the square root of both sides, we obtain

y+19/8=sqrt (89/64) = + or - 1.18

which implies y = - 19/8+or-1.18=2.38+or-1.18

either y = - 2.38+1.18=-1.2

or y = - 2.38-1.18 = - 3.56

Therefore, y=-1.20 or - 3.56