1/2(2x)+1/4(16x)=20

Solution for 1/2(2x)+1/4(16x)=20 equation:

1/2(2x)+1/4(16x)=20

We move all terms to the left:

1/2(2x)+1/4(16x)-(20)=0


Domain of the equation: 22x!=0

x!=0/22

x!=0

x∈R



Domain of the equation: 416x!=0

x!=0/416

x!=0

x∈R


We calculate fractions


416x/9152x^2+22x/9152x^2-20=0

We multiply all the terms by the denominator


416x+22x-20*9152x^2=0

We add all the numbers together, and all the variables

438x-20*9152x^2=0

Wy multiply elements

-183040x^2+438x=0

a = -183040; b = 438; c = 0;
Δ = b2-4ac
Δ = 4382-4·(-183040)·0
Δ = 191844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{191844}=438$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(438)-438}{2*-183040}=\frac{-876}{-366080}
=219/91520
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(438)+438}{2*-183040}=\frac{0}{-366080}
=0
$