Answer:
x=-4 and x=1/2
Step-by-step explanation:
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^{2} +7x=4[/tex]
equate to zero
[tex]2x^{2} +7x-4=0[/tex]
so
[tex]a=2\\b=7\\c=-4[/tex]
substitute in the formula
[tex]x=\frac{-7(+/-)\sqrt{7^{2}-4(2)(-4)}} {2(2)}[/tex]
[tex]x=\frac{-7(+/-)\sqrt{81}} {4}[/tex]
[tex]x=\frac{-7(+/-)9} {4}[/tex]
[tex]x=\frac{-7(+)9} {4}=\frac{1}{2}[/tex]
[tex]x=\frac{-7(-)9} {4}=-4[/tex]
therefore
The solutions are
x=-4 and x=1/2
