(2x+1)+(8/9x+10)=90

Solution for (2x+1)+(8/9x+10)=90 equation:

(2x+1)+(8/9x+10)=90

We move all terms to the left:

(2x+1)+(8/9x+10)-(90)=0


Domain of the equation: 9x+10)!=0

x∈R


We get rid of parentheses

2x+8/9x+1+10-90=0

We multiply all the terms by the denominator


2x*9x+1*9x+10*9x-90*9x+8=0

Wy multiply elements

18x^2+9x+90x-810x+8=0

We add all the numbers together, and all the variables

18x^2-711x+8=0

a = 18; b = -711; c = +8;
Δ = b2-4ac
Δ = -7112-4·18·8
Δ = 504945
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:

$\sqrt{\Delta}=\sqrt{504945}=\sqrt{441*1145}=\sqrt{441}*\sqrt{1145}=21\sqrt{1145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-711)-21\sqrt{1145}}{2*18}=\frac{711-21\sqrt{1145}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-711)+21\sqrt{1145}}{2*18}=\frac{711+21\sqrt{1145}}{36}
$