a)
3x^2+5x=2
3x^2+5x-2=0
ax^2+bx+c=0
a = 3 , b = 5 , c = -2
\Delta=b^2-4ac=5^2-4*3*(-2)=25+24=49
\sqrt\Delta=\sqrt{49}=7
x_1=\frac{-b-\sqrt\Delta}{2a}=\frac{-5-7}{2*3}=\frac{-12}{6}=-2
x_2=\frac{-b+\sqrt\Delta}{2a}=\frac{-5+7}{6}=\frac{2}{6}=\frac{1}{3}
b)
5x-3=2x^2
-2x^2+5x-3=0
ax^2+bx+c=0
a = -2 , b = 5 , c = -3
\Delta=b^2-4ac=5^2-4*(-2)*(-3)=25-24=1
\sqrt\Delta=1
x_1=\frac{-b-\sqrt\Delta}{2a}=\frac{-5-1}{2*(-2)}=\frac{-6}{-4}=\frac{3}{2}
x_2=\frac{-b+\sqrt\Delta}{2a}=\frac{-5+1}{-4}=\frac{-4}{-4}=1