x-(1/2x+50)=120

Solution for x-(1/2x+50)=120 equation:

x-(1/2x+50)=120

We move all terms to the left:

x-(1/2x+50)-(120)=0


Domain of the equation: 2x+50)!=0

x∈R


We get rid of parentheses

x-1/2x-50-120=0

We multiply all the terms by the denominator


x*2x-50*2x-120*2x-1=0

Wy multiply elements

2x^2-100x-240x-1=0

We add all the numbers together, and all the variables

2x^2-340x-1=0

a = 2; b = -340; c = -1;
Δ = b2-4ac
Δ = -3402-4·2·(-1)
Δ = 115608
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:

$\sqrt{\Delta}=\sqrt{115608}=\sqrt{4*28902}=\sqrt{4}*\sqrt{28902}=2\sqrt{28902}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-340)-2\sqrt{28902}}{2*2}=\frac{340-2\sqrt{28902}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-340)+2\sqrt{28902}}{2*2}=\frac{340+2\sqrt{28902}}{4}
$