8.85x-36/5x+12.69=1.25x+7

Solution for 8.85x-36/5x+12.69=1.25x+7 equation:

8.85x-36/5x+12.69=1.25x+7

We move all terms to the left:

8.85x-36/5x+12.69-(1.25x+7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

8.85x-36/5x-1.25x-7+12.69=0

We multiply all the terms by the denominator


(8.85x)*5x-(1.25x)*5x-7*5x+(12.69)*5x-36=0

We add all the numbers together, and all the variables

(+8.85x)*5x-(+1.25x)*5x-7*5x+(12.69)*5x-36=0

We multiply parentheses

40x^2-5x^2-7*5x+63.45x-36=0

Wy multiply elements

40x^2-5x^2-35x+63.45x-36=0

We add all the numbers together, and all the variables

35x^2+28.45x-36=0

a = 35; b = 28.45; c = -36;
Δ = b2-4ac
Δ = 28.452-4·35·(-36)
Δ = 5849.4025
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{-(28.45)-\sqrt{5849.4025}}{2*35}=\frac{-28.45-\sqrt{5849.4025}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28.45)+\sqrt{5849.4025}}{2*35}=\frac{-28.45+\sqrt{5849.4025}}{70}
$