91/2x=-57/10x+152

Solution for 91/2x=-57/10x+152 equation:

91/2x=-57/10x+152

We move all terms to the left:

91/2x-(-57/10x+152)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 10x+152)!=0

x∈R


We get rid of parentheses

91/2x+57/10x-152=0

We calculate fractions


910x/20x^2+114x/20x^2-152=0

We multiply all the terms by the denominator


910x+114x-152*20x^2=0

We add all the numbers together, and all the variables

1024x-152*20x^2=0

Wy multiply elements

-3040x^2+1024x=0

a = -3040; b = 1024; c = 0;
Δ = b2-4ac
Δ = 10242-4·(-3040)·0
Δ = 1048576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1048576}=1024$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1024)-1024}{2*-3040}=\frac{-2048}{-6080}
=32/95
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1024)+1024}{2*-3040}=\frac{0}{-6080}
=0
$