4x=1/4x+70

Solution for 4x=1/4x+70 equation:

4x=1/4x+70

We move all terms to the left:

4x-(1/4x+70)=0


Domain of the equation: 4x+70)!=0

x∈R


We get rid of parentheses

4x-1/4x-70=0

We multiply all the terms by the denominator


4x*4x-70*4x-1=0

Wy multiply elements

16x^2-280x-1=0

a = 16; b = -280; c = -1;
Δ = b2-4ac
Δ = -2802-4·16·(-1)
Δ = 78464
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:

$\sqrt{\Delta}=\sqrt{78464}=\sqrt{64*1226}=\sqrt{64}*\sqrt{1226}=8\sqrt{1226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-8\sqrt{1226}}{2*16}=\frac{280-8\sqrt{1226}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+8\sqrt{1226}}{2*16}=\frac{280+8\sqrt{1226}}{32}
$