7/10x+24=x

Solution for 7/10x+24=x equation:

7/10x+24=x

We move all terms to the left:

7/10x+24-(x)=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+7/10x+24=0

We multiply all the terms by the denominator


-1x*10x+24*10x+7=0

Wy multiply elements

-10x^2+240x+7=0

a = -10; b = 240; c = +7;
Δ = b2-4ac
Δ = 2402-4·(-10)·7
Δ = 57880
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:

$\sqrt{\Delta}=\sqrt{57880}=\sqrt{4*14470}=\sqrt{4}*\sqrt{14470}=2\sqrt{14470}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-2\sqrt{14470}}{2*-10}=\frac{-240-2\sqrt{14470}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+2\sqrt{14470}}{2*-10}=\frac{-240+2\sqrt{14470}}{-20}
$