8/15x+1120=x

Solution for 8/15x+1120=x equation:

8/15x+1120=x

We move all terms to the left:

8/15x+1120-(x)=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+8/15x+1120=0

We multiply all the terms by the denominator


-1x*15x+1120*15x+8=0

Wy multiply elements

-15x^2+16800x+8=0

a = -15; b = 16800; c = +8;
Δ = b2-4ac
Δ = 168002-4·(-15)·8
Δ = 282240480
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:

$\sqrt{\Delta}=\sqrt{282240480}=\sqrt{16*17640030}=\sqrt{16}*\sqrt{17640030}=4\sqrt{17640030}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16800)-4\sqrt{17640030}}{2*-15}=\frac{-16800-4\sqrt{17640030}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16800)+4\sqrt{17640030}}{2*-15}=\frac{-16800+4\sqrt{17640030}}{-30}
$