((2+5\sqrt(5)))/(4)=(1)/(2)*(3+2\sqrt(5))*x*(sin30)
You asked:
Solve the equation \(\frac{2 + 5 \cdot \sqrt{5}}{4} = \frac{1}{2} \cdot \left(3 + 2 \cdot \sqrt{5}\right) \cdot x \cdot \sin\left( 30 \right)\) for the variable \(x\).
MathBot Answer:
The solution is: \[x = \frac{2 + 5 \sqrt{5}}{2 \cdot \left(3 + 2 \sqrt{5}\right) \sin{\left(30 \right)}} \approx -0.89264958\]
\[\begin{aligned}\frac{1}{2} + \frac{5 \sqrt{5}}{4} &= x \left(\sqrt{5} \sin{\left(30 \right)} + \frac{3 \sin{\left(30 \right)}}{2}\right)\\x \left(- \frac{3 \sin{\left(30 \right)}}{2} - \sqrt{5} \sin{\left(30 \right)}\right) &= - \frac{5 \sqrt{5}}{4} - \frac{1}{2}\\x &= \frac{- \frac{5 \sqrt{5}}{4} - \frac{1}{2}}{- \frac{3 \sin{\left(30 \right)}}{2} - \sqrt{5} \sin{\left(30 \right)}}\end{aligned}\]