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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


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

We calculate fractions


80x^2/80x^2+64x/80x^2+60x/80x^2-10=0

Fractions to decimals

64x/80x^2+60x/80x^2-10+1=0

We multiply all the terms by the denominator


64x+60x-10*80x^2+1*80x^2=0

We add all the numbers together, and all the variables

124x-10*80x^2+1*80x^2=0

Wy multiply elements

-800x^2+80x^2+124x=0

We add all the numbers together, and all the variables

-720x^2+124x=0

a = -720; b = 124; c = 0;
Δ = b2-4ac
Δ = 1242-4·(-720)·0
Δ = 15376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15376}=124$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(124)-124}{2*-720}=\frac{-248}{-1440}
=31/180
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(124)+124}{2*-720}=\frac{0}{-1440}
=0
$