3/2x+20=2x-53

Solution for 3/2x+20=2x-53 equation:

3/2x+20=2x-53

We move all terms to the left:

3/2x+20-(2x-53)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-2x+53+20=0

We multiply all the terms by the denominator


-2x*2x+53*2x+20*2x+3=0

Wy multiply elements

-4x^2+106x+40x+3=0

We add all the numbers together, and all the variables

-4x^2+146x+3=0

a = -4; b = 146; c = +3;
Δ = b2-4ac
Δ = 1462-4·(-4)·3
Δ = 21364
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:

$\sqrt{\Delta}=\sqrt{21364}=\sqrt{196*109}=\sqrt{196}*\sqrt{109}=14\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(146)-14\sqrt{109}}{2*-4}=\frac{-146-14\sqrt{109}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(146)+14\sqrt{109}}{2*-4}=\frac{-146+14\sqrt{109}}{-8}
$