4+1/4x+3=10x

Solution for 4+1/4x+3=10x equation:

4+1/4x+3=10x

We move all terms to the left:

4+1/4x+3-(10x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-10x+1/4x+7=0

We multiply all the terms by the denominator


-10x*4x+7*4x+1=0

Wy multiply elements

-40x^2+28x+1=0

a = -40; b = 28; c = +1;
Δ = b2-4ac
Δ = 282-4·(-40)·1
Δ = 944
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:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{59}}{2*-40}=\frac{-28-4\sqrt{59}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{59}}{2*-40}=\frac{-28+4\sqrt{59}}{-80}
$