a)
4(x-5)(2x+3)=0|:4
(x-5)(2x+3)=0
x-5=0 \vee 2x+3=0
x=5 \vee 2x=-3
x_1=-5 , x_2=-\frac{3}{2}=-1,5
b)
(x+1)^2+(2x-4)(2x+4)=0 wzory: 1) (a+b)^2=a^2+2ab+b^2 , 2) (a-b)(a+b)=a^2-b^2
x^2+2x+1+4x^2-16=0
5x^2+2x-15=0
a=5, b=2, c=-15
\Delta=b^2-4ac=4-4*5*(-15)=4+300=304
\sqrt\Delta=\sqrt{304}=\sqrt{16*19}=4\sqrt{19}
x_1=\frac{-b-\sqrt\Delta}{2a}=\frac{-2-4\sqrt{19}}{2*5}=\frac{2(-1-2\sqrt{19)}}{2*5}=\frac{-1-2\sqrt{19}}{5}
x_2=\frac{-b+\sqrt\Delta}{2a}=\frac{-2+4\sqrt{19}}{2*5}=\frac{2(2\sqrt{19}-1)}{2*5}=\frac{2\sqrt{19}-1}{5}