1/2x+4+(3x+5)=97.5

Solution for 1/2x+4+(3x+5)=97.5 equation:

1/2x+4+(3x+5)=97.5

We move all terms to the left:

1/2x+4+(3x+5)-(97.5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+(3x+5)-93.5=0

We get rid of parentheses

1/2x+3x+5-93.5=0

We multiply all the terms by the denominator


3x*2x+5*2x-(93.5)*2x+1=0

We multiply parentheses

3x*2x+5*2x-187x+1=0

Wy multiply elements

6x^2+10x-187x+1=0

We add all the numbers together, and all the variables

6x^2-177x+1=0

a = 6; b = -177; c = +1;
Δ = b2-4ac
Δ = -1772-4·6·1
Δ = 31305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-177)-\sqrt{31305}}{2*6}=\frac{177-\sqrt{31305}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-177)+\sqrt{31305}}{2*6}=\frac{177+\sqrt{31305}}{12}
$