4/5x-5/2=-9/10x-7

Solution for 4/5x-5/2=-9/10x-7 equation:

4/5x-5/2=-9/10x-7

We move all terms to the left:

4/5x-5/2-(-9/10x-7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x-7)!=0

x∈R


We get rid of parentheses

4/5x+9/10x+7-5/2=0

We calculate fractions


(-250x^2)/200x^2+160x/200x^2+180x/200x^2+7=0

We multiply all the terms by the denominator


(-250x^2)+160x+180x+7*200x^2=0

We add all the numbers together, and all the variables

(-250x^2)+340x+7*200x^2=0

Wy multiply elements

(-250x^2)+1400x^2+340x=0

We get rid of parentheses

-250x^2+1400x^2+340x=0

We add all the numbers together, and all the variables

1150x^2+340x=0

a = 1150; b = 340; c = 0;
Δ = b2-4ac
Δ = 3402-4·1150·0
Δ = 115600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{115600}=340$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(340)-340}{2*1150}=\frac{-680}{2300}
=-34/115
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(340)+340}{2*1150}=\frac{0}{2300}
=0
$