x-26=1/2x+13=3x-77

Solution for x-26=1/2x+13=3x-77 equation:

x-26=1/2x+13=3x-77

We move all terms to the left:

x-26-(1/2x+13)=0


Domain of the equation: 2x+13)!=0

x∈R


We get rid of parentheses

x-1/2x-13-26=0

We multiply all the terms by the denominator


x*2x-13*2x-26*2x-1=0

Wy multiply elements

2x^2-26x-52x-1=0

We add all the numbers together, and all the variables

2x^2-78x-1=0

a = 2; b = -78; c = -1;
Δ = b2-4ac
Δ = -782-4·2·(-1)
Δ = 6092
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:

$\sqrt{\Delta}=\sqrt{6092}=\sqrt{4*1523}=\sqrt{4}*\sqrt{1523}=2\sqrt{1523}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1523}}{2*2}=\frac{78-2\sqrt{1523}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1523}}{2*2}=\frac{78+2\sqrt{1523}}{4}
$