9/10x-x-19=-28

Solution for 9/10x-x-19=-28 equation:

9/10x-x-19=-28

We move all terms to the left:

9/10x-x-19-(-28)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+9/10x+9=0

We multiply all the terms by the denominator


-1x*10x+9*10x+9=0

Wy multiply elements

-10x^2+90x+9=0

a = -10; b = 90; c = +9;
Δ = b2-4ac
Δ = 902-4·(-10)·9
Δ = 8460
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:

$\sqrt{\Delta}=\sqrt{8460}=\sqrt{36*235}=\sqrt{36}*\sqrt{235}=6\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{235}}{2*-10}=\frac{-90-6\sqrt{235}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{235}}{2*-10}=\frac{-90+6\sqrt{235}}{-20}
$