3/4x+5=180-x

Solution for 3/4x+5=180-x equation:

3/4x+5=180-x

We move all terms to the left:

3/4x+5-(180-x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(-1x+180)+5=0

We get rid of parentheses

3/4x+1x-180+5=0

We multiply all the terms by the denominator


1x*4x-180*4x+5*4x+3=0

Wy multiply elements

4x^2-720x+20x+3=0

We add all the numbers together, and all the variables

4x^2-700x+3=0

a = 4; b = -700; c = +3;
Δ = b2-4ac
Δ = -7002-4·4·3
Δ = 489952
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:

$\sqrt{\Delta}=\sqrt{489952}=\sqrt{16*30622}=\sqrt{16}*\sqrt{30622}=4\sqrt{30622}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-700)-4\sqrt{30622}}{2*4}=\frac{700-4\sqrt{30622}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-700)+4\sqrt{30622}}{2*4}=\frac{700+4\sqrt{30622}}{8}
$