Solve 4y^2-12y-3 - ScanMath

Evaluate

4 y^{2} - 12 y - 3

To find the roots of the expression,set the expression equal to 0

4 y^{2} - 12 y - 3 = 0

Substitute a= 4,b= - 12 and c= - 3 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 4 ( - 3 )}{2 \times 4}

Simplify the expression

y = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 4 ( - 3 )}{8}

Simplify the expression

More Steps

y = \frac{12 \pm 192}{8}

Simplify the radical expression

More Steps

y = \frac{12 \pm 8 3}{8}

Separate the equation into 2 possible cases

y = \frac{12 + 8 3}{8} y = \frac{12 - 8 3}{8}

Simplify the expression

More Steps

y = \frac{3 + 2 3}{2} y = \frac{12 - 8 3}{8}

Simplify the expression

More Steps

y = \frac{3 + 2 3}{2} y = \frac{3 - 2 3}{2}

Solution

y_{1} = \frac{3 - 2 3}{2}, y_{2} = \frac{3 + 2 3}{2}

Alternative Form

y_{1} \approx - 0.232051, y_{2} \approx 3.232051

Find the roots