Question

Will give brainliest!

Answer 1

So when does y1 = y2?

at
2 (5x + 3) = (x2 -15)

solve and advise answer in comments and will assist further

Answer 2

Solution

The equation of two curves are

     $y_{1}=y=2 \times (5 x+3)\\\\y_{2}=y=x^2-15$

Equating the two curves that is y values, to find their point of Intersection

→  2 × (5 x+3)=x²-15

→10 x +6=x²-15⇒⇒Used distributive property of multiplication with respect to addition

→x² -10 x -15 -6=0

→x² -10 x-21=0

For a Quadratic equation of the type

   $\rightarrow ax^2+b x +c=0\\\\x=\frac{-b \pm \sqrt{D}}{2 a}\\\\D=b^2-4ac$  

Using discriminant method to solve the problem

   $x=\frac{-(-10)\pm\sqrt{(-10)^2-4 \times 1 \times (-21)}}{2 \times 1}\\\\x=\frac{10 \pm \sqrt{100+84}}{2}\\\\x=\frac{10 \pm \sqrt{184}}{2}\\\\x=5 \pm \sqrt{46}\\\\x_{1}=5+6.78\\\\x_{1}=11.78\\\\x_{2}=5-6.78\\\\x_{2}=-1.78$

The x coordinate of point of intersection are, 11.78 and -1.78.