Answer:
[tex]-5x^2+2x+7=-3x+4[/tex]
Step-by-step explanation:
[tex]f(x)=-5x^2+2x+7[/tex]
[tex]g(x)=-3x+4[/tex]
To solve the system of equations, equate the equations:
[tex]\begin{aligned} f(x) &=g(x)\\\implies -5x^2+2x+7&=-3x+4\\-5x^2+2x+7+3x-4 & =0\\-5x^2+5x+3 & =0\\5x^2-5x-3 & =0\end{aligned}[/tex]
Use the quadratic formula to solve for x
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\implies x=\dfrac{-(-5) \pm \sqrt{(-5)^2-4(5)(-3)} }{2(5)}[/tex]
[tex]\implies x=\dfrac{5 \pm \sqrt{85}}{10}[/tex]
