If rx5x23x4and kx2x210x6find all real xvalues such that rxkx

If r(x)=5x2+3x4and k(x)=2x210x+6,find all real x-values such that r(x)=k(x).

x=

Solution

r(x)=5x²+3x-4 and k(x)= 2x²-10x+6

r(x)=k(x)

5x²+3x-4=2x²-10x+6

3x²+13x-10=0

3x²+15x-2x-10=0

3x(x+5)-2(x+5)=0

(3x-2)(x+5)=0

x=2/3 , -5