5/7x-45=8x+52

Solution for 5/7x-45=8x+52 equation:

5/7x-45=8x+52

We move all terms to the left:

5/7x-45-(8x+52)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

5/7x-8x-52-45=0

We multiply all the terms by the denominator


-8x*7x-52*7x-45*7x+5=0

Wy multiply elements

-56x^2-364x-315x+5=0

We add all the numbers together, and all the variables

-56x^2-679x+5=0

a = -56; b = -679; c = +5;
Δ = b2-4ac
Δ = -6792-4·(-56)·5
Δ = 462161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-679)-\sqrt{462161}}{2*-56}=\frac{679-\sqrt{462161}}{-112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-679)+\sqrt{462161}}{2*-56}=\frac{679+\sqrt{462161}}{-112}
$