x=24/10x+7

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

x=24/10x+7

We move all terms to the left:

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


Domain of the equation: 10x+7)!=0

x∈R


We get rid of parentheses

x-24/10x-7=0

We multiply all the terms by the denominator


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

Wy multiply elements

10x^2-70x-24=0

a = 10; b = -70; c = -24;
Δ = b2-4ac
Δ = -702-4·10·(-24)
Δ = 5860
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:

$\sqrt{\Delta}=\sqrt{5860}=\sqrt{4*1465}=\sqrt{4}*\sqrt{1465}=2\sqrt{1465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1465}}{2*10}=\frac{70-2\sqrt{1465}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1465}}{2*10}=\frac{70+2\sqrt{1465}}{20}
$