0.5x+8/7x=x+37

Solution for 0.5x+8/7x=x+37 equation:

0.5x+8/7x=x+37

We move all terms to the left:

0.5x+8/7x-(x+37)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

0.5x+8/7x-x-37=0

We multiply all the terms by the denominator


(0.5x)*7x-x*7x-37*7x+8=0

We add all the numbers together, and all the variables

(+0.5x)*7x-x*7x-37*7x+8=0

We multiply parentheses

0x^2-x*7x-37*7x+8=0

Wy multiply elements

0x^2-7x^2-259x+8=0

We add all the numbers together, and all the variables

-6x^2-259x+8=0

a = -6; b = -259; c = +8;
Δ = b2-4ac
Δ = -2592-4·(-6)·8
Δ = 67273
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{-(-259)-\sqrt{67273}}{2*-6}=\frac{259-\sqrt{67273}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-259)+\sqrt{67273}}{2*-6}=\frac{259+\sqrt{67273}}{-12}
$