(3/2x+20)-2x=90

Solution for (3/2x+20)-2x=90 equation:

(3/2x+20)-2x=90

We move all terms to the left:

(3/2x+20)-2x-(90)=0


Domain of the equation: 2x+20)!=0

x∈R


We add all the numbers together, and all the variables

-2x+(3/2x+20)-90=0

We get rid of parentheses

-2x+3/2x+20-90=0

We multiply all the terms by the denominator


-2x*2x+20*2x-90*2x+3=0

Wy multiply elements

-4x^2+40x-180x+3=0

We add all the numbers together, and all the variables

-4x^2-140x+3=0

a = -4; b = -140; c = +3;
Δ = b2-4ac
Δ = -1402-4·(-4)·3
Δ = 19648
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:

$\sqrt{\Delta}=\sqrt{19648}=\sqrt{64*307}=\sqrt{64}*\sqrt{307}=8\sqrt{307}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-8\sqrt{307}}{2*-4}=\frac{140-8\sqrt{307}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+8\sqrt{307}}{2*-4}=\frac{140+8\sqrt{307}}{-8}
$