3/4x+20=26x-16

Solution for 3/4x+20=26x-16 equation:

3/4x+20=26x-16

We move all terms to the left:

3/4x+20-(26x-16)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-26x+16+20=0

We multiply all the terms by the denominator


-26x*4x+16*4x+20*4x+3=0

Wy multiply elements

-104x^2+64x+80x+3=0

We add all the numbers together, and all the variables

-104x^2+144x+3=0

a = -104; b = 144; c = +3;
Δ = b2-4ac
Δ = 1442-4·(-104)·3
Δ = 21984
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:

$\sqrt{\Delta}=\sqrt{21984}=\sqrt{16*1374}=\sqrt{16}*\sqrt{1374}=4\sqrt{1374}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-4\sqrt{1374}}{2*-104}=\frac{-144-4\sqrt{1374}}{-208}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+4\sqrt{1374}}{2*-104}=\frac{-144+4\sqrt{1374}}{-208}
$