5/8x-8=2x-53

Solution for 5/8x-8=2x-53 equation:

5/8x-8=2x-53

We move all terms to the left:

5/8x-8-(2x-53)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

5/8x-2x+53-8=0

We multiply all the terms by the denominator


-2x*8x+53*8x-8*8x+5=0

Wy multiply elements

-16x^2+424x-64x+5=0

We add all the numbers together, and all the variables

-16x^2+360x+5=0

a = -16; b = 360; c = +5;
Δ = b2-4ac
Δ = 3602-4·(-16)·5
Δ = 129920
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{129920}=\sqrt{64*2030}=\sqrt{64}*\sqrt{2030}=8\sqrt{2030}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-8\sqrt{2030}}{2*-16}=\frac{-360-8\sqrt{2030}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+8\sqrt{2030}}{2*-16}=\frac{-360+8\sqrt{2030}}{-32}
$