90-(1/2x+14)=2x-50

Solution for 90-(1/2x+14)=2x-50 equation:

90-(1/2x+14)=2x-50

We move all terms to the left:

90-(1/2x+14)-(2x-50)=0


Domain of the equation: 2x+14)!=0

x∈R


We get rid of parentheses

-1/2x-2x-14+50+90=0

We multiply all the terms by the denominator


-2x*2x-14*2x+50*2x+90*2x-1=0

Wy multiply elements

-4x^2-28x+100x+180x-1=0

We add all the numbers together, and all the variables

-4x^2+252x-1=0

a = -4; b = 252; c = -1;
Δ = b2-4ac
Δ = 2522-4·(-4)·(-1)
Δ = 63488
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:

$\sqrt{\Delta}=\sqrt{63488}=\sqrt{1024*62}=\sqrt{1024}*\sqrt{62}=32\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-32\sqrt{62}}{2*-4}=\frac{-252-32\sqrt{62}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+32\sqrt{62}}{2*-4}=\frac{-252+32\sqrt{62}}{-8}
$