-1/4x+80=-2x+10

Solution for -1/4x+80=-2x+10 equation:

-1/4x+80=-2x+10

We move all terms to the left:

-1/4x+80-(-2x+10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

-1/4x+2x-10+80=0

We multiply all the terms by the denominator


2x*4x-10*4x+80*4x-1=0

Wy multiply elements

8x^2-40x+320x-1=0

We add all the numbers together, and all the variables

8x^2+280x-1=0

a = 8; b = 280; c = -1;
Δ = b2-4ac
Δ = 2802-4·8·(-1)
Δ = 78432
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:

$\sqrt{\Delta}=\sqrt{78432}=\sqrt{16*4902}=\sqrt{16}*\sqrt{4902}=4\sqrt{4902}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-4\sqrt{4902}}{2*8}=\frac{-280-4\sqrt{4902}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+4\sqrt{4902}}{2*8}=\frac{-280+4\sqrt{4902}}{16}
$