10+x=5(1/5x+3)

Solution for 10+x=5(1/5x+3) equation:

10+x=5(1/5x+3)

We move all terms to the left:

10+x-(5(1/5x+3))=0


Domain of the equation: 5x+3))!=0

x∈R


We multiply all the terms by the denominator


x*5x+10*5x+3))-(5(1+3))=0

We add all the numbers together, and all the variables

x*5x+10*5x+3))-(54)=0

We add all the numbers together, and all the variables

x*5x+10*5x=0

Wy multiply elements

5x^2+50x=0

a = 5; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·5·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-50}{2*5}=\frac{-100}{10}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*5}=\frac{0}{10}
=0
$