21/2x+3/4x=26

Solution for 21/2x+3/4x=26 equation:

21/2x+3/4x=26

We move all terms to the left:

21/2x+3/4x-(26)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


84x/8x^2+6x/8x^2-26=0

We multiply all the terms by the denominator


84x+6x-26*8x^2=0

We add all the numbers together, and all the variables

90x-26*8x^2=0

Wy multiply elements

-208x^2+90x=0

a = -208; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·(-208)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*-208}=\frac{-180}{-416}
=45/104
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*-208}=\frac{0}{-416}
=0
$