1/4x+10=5x+3

Solution for 1/4x+10=5x+3 equation:

1/4x+10=5x+3

We move all terms to the left:

1/4x+10-(5x+3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-5x-3+10=0

We multiply all the terms by the denominator


-5x*4x-3*4x+10*4x+1=0

Wy multiply elements

-20x^2-12x+40x+1=0

We add all the numbers together, and all the variables

-20x^2+28x+1=0

a = -20; b = 28; c = +1;
Δ = b2-4ac
Δ = 282-4·(-20)·1
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-12\sqrt{6}}{2*-20}=\frac{-28-12\sqrt{6}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+12\sqrt{6}}{2*-20}=\frac{-28+12\sqrt{6}}{-40}
$