Solve for all solutions of \( x \) \( x^{2}+6 x-15=0 \)

Solve the equation \( x^{2}+6x-15=0 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(x^{2}+6x-15=0\) - step1: Solve using the quadratic formula: \(x=\frac{-6\pm \sqrt{6^{2}-4\left(-15\right)}}{2}\) - step2: Simplify the expression: \(x=\frac{-6\pm \sqrt{96}}{2}\) - step3: Simplify the expression: \(x=\frac{-6\pm 4\sqrt{6}}{2}\) - step4: Separate into possible cases: \(\begin{align}&x=\frac{-6+4\sqrt{6}}{2}\\&x=\frac{-6-4\sqrt{6}}{2}\end{align}\) - step5: Simplify the expression: \(\begin{align}&x=-3+2\sqrt{6}\\&x=\frac{-6-4\sqrt{6}}{2}\end{align}\) - step6: Simplify the expression: \(\begin{align}&x=-3+2\sqrt{6}\\&x=-3-2\sqrt{6}\end{align}\) - step7: Rewrite: \(x_{1}=-3-2\sqrt{6},x_{2}=-3+2\sqrt{6}\) The solutions to the equation \(x^{2}+6x-15=0\) are \(x_{1}=-3-2\sqrt{6}\) and \(x_{2}=-3+2\sqrt{6}\).