3/(5x+10)+2(x+3)=22

Solution for 3/(5x+10)+2(x+3)=22 equation:

3/(5x+10)+2(x+3)=22

We move all terms to the left:

3/(5x+10)+2(x+3)-(22)=0


Domain of the equation: (5x+10)!=0

We move all terms containing x to the left, all other terms to the right

5x!=-10

x!=-10/5

x!=-2

x∈R


We multiply parentheses

3/(5x+10)+2x+6-22=0

We multiply all the terms by the denominator


2x*(5x+10)+6*(5x+10)-22*(5x+10)+3=0

We multiply parentheses

10x^2+20x+30x-110x+60-220+3=0

We add all the numbers together, and all the variables

10x^2-60x-157=0

a = 10; b = -60; c = -157;
Δ = b2-4ac
Δ = -602-4·10·(-157)
Δ = 9880
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:

$\sqrt{\Delta}=\sqrt{9880}=\sqrt{4*2470}=\sqrt{4}*\sqrt{2470}=2\sqrt{2470}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{2470}}{2*10}=\frac{60-2\sqrt{2470}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{2470}}{2*10}=\frac{60+2\sqrt{2470}}{20}
$