Respuesta:
x = 11/8 , x =5
Explicación paso a paso:
3x - [(2x-5)²]/2 = (5+x)/4
[6x - (2x-5)²]/2 = (5+x)/4
4[6x - (2x-5)²] = 2(5+x)
24x - 4(2x-5)² = 10 + 2x
24x - 4(4x²-20x+25) = 10 + 2x
24x - 16x² + 80x - 100 = 10+ 2x
-16x ² +24x+80x-2x-10-100 =0
-16x²+102x -110 =0
-8x²+51x-55 =0
Formual general:
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Donde:
a= -8
b = 51
c = -55
[tex]x_{1,\:2}=\frac{-51\pm \sqrt{51^2-4\left(-8\right)\left(-55\right)}}{2\left(-8\right)}\\\\x_{1,\:2}=\frac{-51\pm \:29}{2\left(-8\right)}\\[/tex]
Separa las soluciones:
[tex]x_1=\frac{-51+29}{2\left(-8\right)},\:x_2=\frac{-51-29}{2\left(-8\right)}\\\\x=\frac{11}{8},\:x=5[/tex]
