résoudre 2(x-5)²-7(x-5)=0 (x+8)(2x-1)=(3x-5)(7x-3)

(x-5)[2(x-5)-7]=0
(x-5)(2x-10-7)=0
(x-5)(2x-17)=0

x-5=0
x=5

2x-17=0
2x=17
x=17/2

(x+8)(2x-1)=(3x-5)(7x-3)
2x^2-x+16x-8=21x^2-9x-35x+15
21x^2-2x^2-44x-16x+15+8=0
19x^2-60x+23=0

Delta = (-60)^2-4*19*23
Delta = 3600-1748
Delta= 1852 > 0 donc deux solutions

x1=(60-V1852)/(2*19)
x1=(60-2V463)/38
x1=(30-V463)/19

x2=(60+V1852)/38
x2=(30+V463)/19