3(x+9x)(5+4x)=26+x

Solution for 3(x+9x)(5+4x)=26+x equation:

3(x+9x)(5+4x)=26+x

We move all terms to the left:

3(x+9x)(5+4x)-(26+x)=0

We add all the numbers together, and all the variables

3(+10x)(4x+5)-(x+26)=0

We get rid of parentheses

3(+10x)(4x+5)-x-26=0

We multiply parentheses ..

3(+40x^2+50x)-x-26=0

We add all the numbers together, and all the variables

3(+40x^2+50x)-1x-26=0

We multiply parentheses

120x^2+150x-1x-26=0

We add all the numbers together, and all the variables

120x^2+149x-26=0

a = 120; b = 149; c = -26;
Δ = b2-4ac
Δ = 1492-4·120·(-26)
Δ = 34681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(149)-\sqrt{34681}}{2*120}=\frac{-149-\sqrt{34681}}{240}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(149)+\sqrt{34681}}{2*120}=\frac{-149+\sqrt{34681}}{240}
$