75x+10-0.5=2(1/8x+5)

Solution for 75x+10-0.5=2(1/8x+5) equation:

75x+10-0.5=2(1/8x+5)

We move all terms to the left:

75x+10-0.5-(2(1/8x+5))=0


Domain of the equation: 8x+5))!=0

x∈R


We add all the numbers together, and all the variables

75x-(2(1/8x+5))+9.5=0

We multiply all the terms by the denominator


75x*8x+(9.5)*8x+5))-(2(1+5))=0

We add all the numbers together, and all the variables

75x*8x+(9.5)*8x+5))-(26)=0

We add all the numbers together, and all the variables

75x*8x+(9.5)*8x=0

We multiply parentheses

75x*8x+76x=0

Wy multiply elements

600x^2+76x=0

a = 600; b = 76; c = 0;
Δ = b2-4ac
Δ = 762-4·600·0
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-76}{2*600}=\frac{-152}{1200}
=-19/150
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+76}{2*600}=\frac{0}{1200}
=0
$