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

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



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

We move all terms to the left:

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



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R





Domain of the equation: 2x-5)!=0

x∈R



We get rid of parentheses

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

We calculate fractions


(-6x)/8x^2+4x/8x^2+5+10=0

We add all the numbers together, and all the variables

(-6x)/8x^2+4x/8x^2+15=0

We multiply all the terms by the denominator


(-6x)+4x+15*8x^2=0

We add all the numbers together, and all the variables

4x+(-6x)+15*8x^2=0

Wy multiply elements

120x^2+4x+(-6x)=0

We get rid of parentheses

120x^2+4x-6x=0

We add all the numbers together, and all the variables

120x^2-2x=0

a = 120; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·120·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*120}=\frac{0}{240}
=0
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*120}=\frac{4}{240}
=1/60
$

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