0.875x-0.5=3/16x+5

Solution for 0.875x-0.5=3/16x+5 equation:

0.875x-0.5=3/16x+5

We move all terms to the left:

0.875x-0.5-(3/16x+5)=0


Domain of the equation: 16x+5)!=0

x∈R


We get rid of parentheses

0.875x-3/16x-5-0.5=0

We multiply all the terms by the denominator


(0.875x)*16x-5*16x-(0.5)*16x-3=0

We add all the numbers together, and all the variables

(+0.875x)*16x-5*16x-(0.5)*16x-3=0

We multiply parentheses

0x^2-5*16x-8x-3=0

Wy multiply elements

0x^2-80x-8x-3=0

We add all the numbers together, and all the variables

x^2-88x-3=0

a = 1; b = -88; c = -3;
Δ = b2-4ac
Δ = -882-4·1·(-3)
Δ = 7756
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:

$\sqrt{\Delta}=\sqrt{7756}=\sqrt{4*1939}=\sqrt{4}*\sqrt{1939}=2\sqrt{1939}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-2\sqrt{1939}}{2*1}=\frac{88-2\sqrt{1939}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+2\sqrt{1939}}{2*1}=\frac{88+2\sqrt{1939}}{2}
$