solve the quadratic equation.\n-3x² + 5x - 7 = 0\nwrite one exact solution in each box. you can add or…

Explanation:

Step1: Identify coefficients

For the quadratic equation $-3x^{2}+5x - 7=0$, we have $a=-3$, $b = 5$, $c=-7$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac$. Substitute the values: $\Delta=(5)^{2}-4\times(-3)\times(-7)=25 - 84=- 59$.

Step3: Use the quadratic - formula

The quadratic formula is $x=\frac{-b\pm\sqrt{\Delta}}{2a}$. Since $\Delta=-59<0$, there are no real solutions. In the complex - number system, $x=\frac{-5\pm\sqrt{59}i}{-6}=\frac{5\pm\sqrt{59}i}{6}$.

Answer:

$x=\frac{5 + \sqrt{59}i}{6}$, $x=\frac{5-\sqrt{59}i}{6}$