1/2+4/5x=3/2x+7

Solution for 1/2+4/5x=3/2x+7 equation:

1/2+4/5x=3/2x+7

We move all terms to the left:

1/2+4/5x-(3/2x+7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x+7)!=0

x∈R


We get rid of parentheses

4/5x-3/2x-7+1/2=0

We calculate fractions


32x/40x^2+(-15x)/40x^2+5x/40x^2-7=0

We multiply all the terms by the denominator


32x+(-15x)+5x-7*40x^2=0

We add all the numbers together, and all the variables

37x+(-15x)-7*40x^2=0

Wy multiply elements

-280x^2+37x+(-15x)=0

We get rid of parentheses

-280x^2+37x-15x=0

We add all the numbers together, and all the variables

-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
$