.5x+10=1/4x+54

Solution for .5x+10=1/4x+54 equation:

.5x+10=1/4x+54

We move all terms to the left:

.5x+10-(1/4x+54)=0


Domain of the equation: 4x+54)!=0

x∈R


We get rid of parentheses

.5x-1/4x-54+10=0

We multiply all the terms by the denominator


(.5x)*4x-54*4x+10*4x-1=0

We add all the numbers together, and all the variables

(+.5x)*4x-54*4x+10*4x-1=0

We multiply parentheses

4x^2-54*4x+10*4x-1=0

Wy multiply elements

4x^2-216x+40x-1=0

We add all the numbers together, and all the variables

4x^2-176x-1=0

a = 4; b = -176; c = -1;
Δ = b2-4ac
Δ = -1762-4·4·(-1)
Δ = 30992
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:

$\sqrt{\Delta}=\sqrt{30992}=\sqrt{16*1937}=\sqrt{16}*\sqrt{1937}=4\sqrt{1937}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-4\sqrt{1937}}{2*4}=\frac{176-4\sqrt{1937}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+4\sqrt{1937}}{2*4}=\frac{176+4\sqrt{1937}}{8}
$