2/5x+10=x+19

Solution for 2/5x+10=x+19 equation:

2/5x+10=x+19

We move all terms to the left:

2/5x+10-(x+19)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-x-19+10=0

We multiply all the terms by the denominator


-x*5x-19*5x+10*5x+2=0

Wy multiply elements

-5x^2-95x+50x+2=0

We add all the numbers together, and all the variables

-5x^2-45x+2=0

a = -5; b = -45; c = +2;
Δ = b2-4ac
Δ = -452-4·(-5)·2
Δ = 2065
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{2065}}{2*-5}=\frac{45-\sqrt{2065}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2065}}{2*-5}=\frac{45+\sqrt{2065}}{-10}
$