(5/2x-5)+(4x)=180

Solution for (5/2x-5)+(4x)=180 equation:

(5/2x-5)+(4x)=180

We move all terms to the left:

(5/2x-5)+(4x)-(180)=0


Domain of the equation: 2x-5)!=0

x∈R


We add all the numbers together, and all the variables

4x+(5/2x-5)-180=0

We get rid of parentheses

4x+5/2x-5-180=0

We multiply all the terms by the denominator


4x*2x-5*2x-180*2x+5=0

Wy multiply elements

8x^2-10x-360x+5=0

We add all the numbers together, and all the variables

8x^2-370x+5=0

a = 8; b = -370; c = +5;
Δ = b2-4ac
Δ = -3702-4·8·5
Δ = 136740
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:

$\sqrt{\Delta}=\sqrt{136740}=\sqrt{4*34185}=\sqrt{4}*\sqrt{34185}=2\sqrt{34185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-370)-2\sqrt{34185}}{2*8}=\frac{370-2\sqrt{34185}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-370)+2\sqrt{34185}}{2*8}=\frac{370+2\sqrt{34185}}{16}
$