10x=-1/4x+12

Solution for 10x=-1/4x+12 equation:

10x=-1/4x+12

We move all terms to the left:

10x-(-1/4x+12)=0


Domain of the equation: 4x+12)!=0

x∈R


We get rid of parentheses

10x+1/4x-12=0

We multiply all the terms by the denominator


10x*4x-12*4x+1=0

Wy multiply elements

40x^2-48x+1=0

a = 40; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·40·1
Δ = 2144
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:

$\sqrt{\Delta}=\sqrt{2144}=\sqrt{16*134}=\sqrt{16}*\sqrt{134}=4\sqrt{134}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{134}}{2*40}=\frac{48-4\sqrt{134}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{134}}{2*40}=\frac{48+4\sqrt{134}}{80}
$