(5x)+(1/2x+24)=90

Solution for (5x)+(1/2x+24)=90 equation:

(5x)+(1/2x+24)=90

We move all terms to the left:

(5x)+(1/2x+24)-(90)=0


Domain of the equation: 2x+24)!=0

x∈R


We get rid of parentheses

5x+1/2x+24-90=0

We multiply all the terms by the denominator


5x*2x+24*2x-90*2x+1=0

Wy multiply elements

10x^2+48x-180x+1=0

We add all the numbers together, and all the variables

10x^2-132x+1=0

a = 10; b = -132; c = +1;
Δ = b2-4ac
Δ = -1322-4·10·1
Δ = 17384
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:

$\sqrt{\Delta}=\sqrt{17384}=\sqrt{4*4346}=\sqrt{4}*\sqrt{4346}=2\sqrt{4346}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-2\sqrt{4346}}{2*10}=\frac{132-2\sqrt{4346}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+2\sqrt{4346}}{2*10}=\frac{132+2\sqrt{4346}}{20}
$