3/4x+10=5x-1

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

3/4x+10=5x-1

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-20x^2+4x+40x+3=0

We add all the numbers together, and all the variables

-20x^2+44x+3=0

a = -20; b = 44; c = +3;
Δ = b2-4ac
Δ = 442-4·(-20)·3
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-8\sqrt{34}}{2*-20}=\frac{-44-8\sqrt{34}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+8\sqrt{34}}{2*-20}=\frac{-44+8\sqrt{34}}{-40}
$