1/4x+3/10x+2=-5

Solution for 1/4x+3/10x+2=-5 equation:

1/4x+3/10x+2=-5

We move all terms to the left:

1/4x+3/10x+2-(-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x+3/10x+7=0

We calculate fractions


10x/40x^2+12x/40x^2+7=0

We multiply all the terms by the denominator


10x+12x+7*40x^2=0

We add all the numbers together, and all the variables

22x+7*40x^2=0

Wy multiply elements

280x^2+22x=0

a = 280; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·280·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*280}=\frac{-44}{560}
=-11/140
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*280}=\frac{0}{560}
=0
$