30+2x=28/5x+12=20

Solution for 30+2x=28/5x+12=20 equation:

30+2x=28/5x+12=20

We move all terms to the left:

30+2x-(28/5x+12)=0


Domain of the equation: 5x+12)!=0

x∈R


We get rid of parentheses

2x-28/5x-12+30=0

We multiply all the terms by the denominator


2x*5x-12*5x+30*5x-28=0

Wy multiply elements

10x^2-60x+150x-28=0

We add all the numbers together, and all the variables

10x^2+90x-28=0

a = 10; b = 90; c = -28;
Δ = b2-4ac
Δ = 902-4·10·(-28)
Δ = 9220
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:

$\sqrt{\Delta}=\sqrt{9220}=\sqrt{4*2305}=\sqrt{4}*\sqrt{2305}=2\sqrt{2305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2305}}{2*10}=\frac{-90-2\sqrt{2305}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2305}}{2*10}=\frac{-90+2\sqrt{2305}}{20}
$