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5y\times 1\left(4y+3\right)=4
Multiply both sides of the equation by 10, the least common multiple of 2,5.
5y\left(4y+3\right)=4
Multiply 5 and 1 to get 5.
20y^{2}+15y=4
Use the distributive property to multiply 5y by 4y+3.
20y^{2}+15y-4=0
Subtract 4 from both sides.
y=\frac{-15±\sqrt{15^{2}-4\times 20\left(-4\right)}}{2\times 20}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 15 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
y=\frac{-15±\sqrt{225-4\times 20\left(-4\right)}}{2\times 20}
Square 15.
y=\frac{-15±\sqrt{225-80\left(-4\right)}}{2\times 20}
Multiply -4 times 20.
y=\frac{-15±\sqrt{225+320}}{2\times 20}
Multiply -80 times -4.
y=\frac{-15±\sqrt{545}}{2\times 20}
Add 225 to 320.
y=\frac{-15±\sqrt{545}}{40}
Multiply 2 times 20.
y=\frac{\sqrt{545}-15}{40}
Now solve the equation y=\frac{-15±\sqrt{545}}{40} when ± is plus. Add -15 to \sqrt{545}.
y=\frac{\sqrt{545}}{40}-\frac{3}{8}
Divide -15+\sqrt{545} by 40.
y=\frac{-\sqrt{545}-15}{40}
Now solve the equation y=\frac{-15±\sqrt{545}}{40} when ± is minus. Subtract \sqrt{545} from -15.
y=-\frac{\sqrt{545}}{40}-\frac{3}{8}
Divide -15-\sqrt{545} by 40.
y=\frac{\sqrt{545}}{40}-\frac{3}{8} y=-\frac{\sqrt{545}}{40}-\frac{3}{8}
The equation is now solved.
5y\times 1\left(4y+3\right)=4
Multiply both sides of the equation by 10, the least common multiple of 2,5.
5y\left(4y+3\right)=4
Multiply 5 and 1 to get 5.
20y^{2}+15y=4
Use the distributive property to multiply 5y by 4y+3.
\frac{20y^{2}+15y}{20}=\frac{4}{20}
Divide both sides by 20.
y^{2}+\frac{15}{20}y=\frac{4}{20}
Dividing by 20 undoes the multiplication by 20.
y^{2}+\frac{3}{4}y=\frac{4}{20}
Reduce the fraction \frac{15}{20} to lowest terms by extracting and canceling out 5.
y^{2}+\frac{3}{4}y=\frac{1}{5}
Reduce the fraction \frac{4}{20} to lowest terms by extracting and canceling out 4.
y^{2}+\frac{3}{4}y+\left(\frac{3}{8}\right)^{2}=\frac{1}{5}+\left(\frac{3}{8}\right)^{2}
Divide \frac{3}{4}, the coefficient of the x term, by 2 to get \frac{3}{8}. Then add the square of \frac{3}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
y^{2}+\frac{3}{4}y+\frac{9}{64}=\frac{1}{5}+\frac{9}{64}
Square \frac{3}{8} by squaring both the numerator and the denominator of the fraction.
y^{2}+\frac{3}{4}y+\frac{9}{64}=\frac{109}{320}
Add \frac{1}{5} to \frac{9}{64} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(y+\frac{3}{8}\right)^{2}=\frac{109}{320}
Factor y^{2}+\frac{3}{4}y+\frac{9}{64}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(y+\frac{3}{8}\right)^{2}}=\sqrt{\frac{109}{320}}
Take the square root of both sides of the equation.
y+\frac{3}{8}=\frac{\sqrt{545}}{40} y+\frac{3}{8}=-\frac{\sqrt{545}}{40}
Simplify.
y=\frac{\sqrt{545}}{40}-\frac{3}{8} y=-\frac{\sqrt{545}}{40}-\frac{3}{8}
Subtract \frac{3}{8} from both sides of the equation.