1/4x+10=2x-25

Solution for 1/4x+10=2x-25 equation:

1/4x+10=2x-25

We move all terms to the left:

1/4x+10-(2x-25)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-2x+25+10=0

We multiply all the terms by the denominator


-2x*4x+25*4x+10*4x+1=0

Wy multiply elements

-8x^2+100x+40x+1=0

We add all the numbers together, and all the variables

-8x^2+140x+1=0

a = -8; b = 140; c = +1;
Δ = b2-4ac
Δ = 1402-4·(-8)·1
Δ = 19632
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:

$\sqrt{\Delta}=\sqrt{19632}=\sqrt{16*1227}=\sqrt{16}*\sqrt{1227}=4\sqrt{1227}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-4\sqrt{1227}}{2*-8}=\frac{-140-4\sqrt{1227}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+4\sqrt{1227}}{2*-8}=\frac{-140+4\sqrt{1227}}{-16}
$