x=7/12x+35

Solution for x=7/12x+35 equation:

x=7/12x+35

We move all terms to the left:

x-(7/12x+35)=0


Domain of the equation: 12x+35)!=0

x∈R


We get rid of parentheses

x-7/12x-35=0

We multiply all the terms by the denominator


x*12x-35*12x-7=0

Wy multiply elements

12x^2-420x-7=0

a = 12; b = -420; c = -7;
Δ = b2-4ac
Δ = -4202-4·12·(-7)
Δ = 176736
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:

$\sqrt{\Delta}=\sqrt{176736}=\sqrt{16*11046}=\sqrt{16}*\sqrt{11046}=4\sqrt{11046}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-4\sqrt{11046}}{2*12}=\frac{420-4\sqrt{11046}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+4\sqrt{11046}}{2*12}=\frac{420+4\sqrt{11046}}{24}
$