1/2x+10=14x+54

Solution for 1/2x+10=14x+54 equation:

1/2x+10=14x+54

We move all terms to the left:

1/2x+10-(14x+54)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-14x-54+10=0

We multiply all the terms by the denominator


-14x*2x-54*2x+10*2x+1=0

Wy multiply elements

-28x^2-108x+20x+1=0

We add all the numbers together, and all the variables

-28x^2-88x+1=0

a = -28; b = -88; c = +1;
Δ = b2-4ac
Δ = -882-4·(-28)·1
Δ = 7856
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:

$\sqrt{\Delta}=\sqrt{7856}=\sqrt{16*491}=\sqrt{16}*\sqrt{491}=4\sqrt{491}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-4\sqrt{491}}{2*-28}=\frac{88-4\sqrt{491}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+4\sqrt{491}}{2*-28}=\frac{88+4\sqrt{491}}{-56}
$