2x+30=3/2x+50

Solution for 2x+30=3/2x+50 equation:

2x+30=3/2x+50

We move all terms to the left:

2x+30-(3/2x+50)=0


Domain of the equation: 2x+50)!=0

x∈R


We get rid of parentheses

2x-3/2x-50+30=0

We multiply all the terms by the denominator


2x*2x-50*2x+30*2x-3=0

Wy multiply elements

4x^2-100x+60x-3=0

We add all the numbers together, and all the variables

4x^2-40x-3=0

a = 4; b = -40; c = -3;
Δ = b2-4ac
Δ = -402-4·4·(-3)
Δ = 1648
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:

$\sqrt{\Delta}=\sqrt{1648}=\sqrt{16*103}=\sqrt{16}*\sqrt{103}=4\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{103}}{2*4}=\frac{40-4\sqrt{103}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{103}}{2*4}=\frac{40+4\sqrt{103}}{8}
$