7x+10-0.5x=2(1/8x+15)

Solution for 7x+10-0.5x=2(1/8x+15) equation:

7x+10-0.5x=2(1/8x+15)

We move all terms to the left:

7x+10-0.5x-(2(1/8x+15))=0


Domain of the equation: 8x+15))!=0

x∈R


We add all the numbers together, and all the variables

6.5x-(2(1/8x+15))+10=0

We multiply all the terms by the denominator


(6.5x)*8x+10*8x+15))-(2(1+15))=0

We add all the numbers together, and all the variables

(+6.5x)*8x+10*8x+15))-(216)=0

We add all the numbers together, and all the variables

(+6.5x)*8x+10*8x=0

We multiply parentheses

48x^2+10*8x=0

Wy multiply elements

48x^2+80x=0

a = 48; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·48·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-80}{2*48}=\frac{-160}{96}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*48}=\frac{0}{96}
=0
$