(1/4)(40-8x)=19x+2-5x

Solution for (1/4)(40-8x)=19x+2-5x equation:

(1/4)(40-8x)=19x+2-5x

We move all terms to the left:

(1/4)(40-8x)-(19x+2-5x)=0


Domain of the equation: 4)(40-8x)!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)(-8x+40)-(14x+2)=0

We get rid of parentheses

(+1/4)(-8x+40)-14x-2=0

We multiply parentheses ..

(-8x^2+1/4*40)-14x-2=0

We multiply all the terms by the denominator


(-8x^2+1-14x*4*40)-2*4*40)=0

We add all the numbers together, and all the variables

(-8x^2+1-14x*4*40)=0

We get rid of parentheses

-8x^2-14x*4*40+1=0

Wy multiply elements

-8x^2-2240x*4+1=0

Wy multiply elements

-8x^2-8960x+1=0

a = -8; b = -8960; c = +1;
Δ = b2-4ac
Δ = -89602-4·(-8)·1
Δ = 80281632
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80281632}=\sqrt{16*5017602}=\sqrt{16}*\sqrt{5017602}=4\sqrt{5017602}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8960)-4\sqrt{5017602}}{2*-8}=\frac{8960-4\sqrt{5017602}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8960)+4\sqrt{5017602}}{2*-8}=\frac{8960+4\sqrt{5017602}}{-16}
$