8-7/10x+16.5=4x+7.5

Solution for 8-7/10x+16.5=4x+7.5 equation:

8-7/10x+16.5=4x+7.5

We move all terms to the left:

8-7/10x+16.5-(4x+7.5)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

-7/10x-(4x+7.5)+24.5=0

We get rid of parentheses

-7/10x-4x-7.5+24.5=0

We multiply all the terms by the denominator


-4x*10x-(7.5)*10x+(24.5)*10x-7=0

We multiply parentheses

-4x*10x-75x+245x-7=0

Wy multiply elements

-40x^2-75x+245x-7=0

We add all the numbers together, and all the variables

-40x^2+170x-7=0

a = -40; b = 170; c = -7;
Δ = b2-4ac
Δ = 1702-4·(-40)·(-7)
Δ = 27780
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:

$\sqrt{\Delta}=\sqrt{27780}=\sqrt{4*6945}=\sqrt{4}*\sqrt{6945}=2\sqrt{6945}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(170)-2\sqrt{6945}}{2*-40}=\frac{-170-2\sqrt{6945}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(170)+2\sqrt{6945}}{2*-40}=\frac{-170+2\sqrt{6945}}{-80}
$