1/2*3x=4x+20

Solution for 1/2*3x=4x+20 equation:

1/2*3x=4x+20

We move all terms to the left:

1/2*3x-(4x+20)=0


Domain of the equation: 2*3x!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

1/2*3x-4x-20=0

We multiply all the terms by the denominator


-4x*2*3x-20*2*3x+1=0

Wy multiply elements

-24x^2*3-120x*3+1=0

Wy multiply elements

-72x^2-360x+1=0

a = -72; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·(-72)·1
Δ = 129888
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:

$\sqrt{\Delta}=\sqrt{129888}=\sqrt{144*902}=\sqrt{144}*\sqrt{902}=12\sqrt{902}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-12\sqrt{902}}{2*-72}=\frac{360-12\sqrt{902}}{-144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+12\sqrt{902}}{2*-72}=\frac{360+12\sqrt{902}}{-144}
$