4y2 +5y_21=0
do you mean
4 y^2 + 5 y - 21 =0 ??
if so
y = [ -5 +/- sqrt(25 + 336) ] / 8
y = [ -5 +/- 19 ] / 8
y = -24/8 or 14/8 which is -3 or +7/4
(4y+7)(y-3) = 0
To solve the quadratic equation 4y^2 + 5y - 21 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form of ay^2 + by + c = 0, the solutions can be found using the formula:
y = (-b ± √(b^2 - 4ac)) / (2a)
In this case, we have a = 4, b = 5, and c = -21.
Plugging these values into the quadratic formula, we get:
y = (-5 ± √(5^2 - 4*4*(-21))) / (2*4)
Simplifying further:
y = (-5 ± √(25 + 336)) / 8
y = (-5 ± √361) / 8
Now, let's calculate the square root of 361:
√361 = 19
Now we have:
y = (-5 ± 19) / 8
This gives us two possible solutions:
1. y = (-5 + 19) / 8 = 14/8 = 7/4
2. y = (-5 - 19) / 8 = -24/8 = -3
Therefore, the solutions to the quadratic equation 4y^2 + 5y - 21 = 0 are y = 7/4 and y = -3.