Answer:
The roots are -1 and 0.60
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]2x-3=-5x^{2}[/tex]
so
[tex]5x^{2}+2x-3=0[/tex]
[tex]a=5\\b=2\\c=-3[/tex]
substitute in the formula
[tex]x=\frac{-2(+/-)\sqrt{2^{2}-4(5)(-3)}} {2(5)}[/tex]
[tex]x=\frac{-2(+/-)\sqrt{64}} {10}[/tex]
[tex]x=\frac{-2(+/-)8} {10}[/tex]
[tex]x=\frac{-2(+)8} {10}=0.60[/tex]
[tex]x=\frac{-2(-)8} {10}=-1[/tex]
therefore
The roots are -1 and 0.60
