1/2x+2/5x+10=37

Solution for 1/2x+2/5x+10=37 equation:

1/2x+2/5x+10=37

We move all terms to the left:

1/2x+2/5x+10-(37)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+2/5x-27=0

We calculate fractions


5x/10x^2+4x/10x^2-27=0

We multiply all the terms by the denominator


5x+4x-27*10x^2=0

We add all the numbers together, and all the variables

9x-27*10x^2=0

Wy multiply elements

-270x^2+9x=0

a = -270; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-270)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-270}=\frac{-18}{-540}
=1/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-270}=\frac{0}{-540}
=0
$