(90-(1/2x+15))=2x-50

Solution for (90-(1/2x+15))=2x-50 equation:

(90-(1/2x+15))=2x-50

We move all terms to the left:

(90-(1/2x+15))-(2x-50)=0


Domain of the equation: 2x+15))!=0

x∈R


We get rid of parentheses

(90-(1/2x+15))-2x+50=0

We multiply all the terms by the denominator


(90-(1-2x*2x+15))+50*2x+15))=0


We calculate terms in parentheses: +(90-(1-2x*2x+15)), so:

90-(1-2x*2x+15)

determiningTheFunctionDomain
-(1-2x*2x+15)+90

We add all the numbers together, and all the variables

-(-2x*2x+16)+90

We get rid of parentheses

2x*2x-16+90

We add all the numbers together, and all the variables

2x*2x+74

Wy multiply elements

4x^2+74

Back to the equation:

+(4x^2+74)


We add all the numbers together, and all the variables

(4x^2+74)+50*2x=0

Wy multiply elements

(4x^2+74)+100x=0

We get rid of parentheses

4x^2+100x+74=0

a = 4; b = 100; c = +74;
Δ = b2-4ac
Δ = 1002-4·4·74
Δ = 8816
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:

$\sqrt{\Delta}=\sqrt{8816}=\sqrt{16*551}=\sqrt{16}*\sqrt{551}=4\sqrt{551}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{551}}{2*4}=\frac{-100-4\sqrt{551}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{551}}{2*4}=\frac{-100+4\sqrt{551}}{8}
$