53/5x-77/10=62/3x+12

Solution for 53/5x-77/10=62/3x+12 equation:

53/5x-77/10=62/3x+12

We move all terms to the left:

53/5x-77/10-(62/3x+12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x+12)!=0

x∈R


We get rid of parentheses

53/5x-62/3x-12-77/10=0

We calculate fractions


(-3465x^2)/150x^2+1590x/150x^2+(-3100x)/150x^2-12=0

We multiply all the terms by the denominator


(-3465x^2)+1590x+(-3100x)-12*150x^2=0

Wy multiply elements

(-3465x^2)-1800x^2+1590x+(-3100x)=0

We get rid of parentheses

-3465x^2-1800x^2+1590x-3100x=0

We add all the numbers together, and all the variables

-5265x^2-1510x=0

a = -5265; b = -1510; c = 0;
Δ = b2-4ac
Δ = -15102-4·(-5265)·0
Δ = 2280100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2280100}=1510$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1510)-1510}{2*-5265}=\frac{0}{-10530}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1510)+1510}{2*-5265}=\frac{3020}{-10530}
=-302/1053
$