2.25x+3(6)=11/5x-18

Solution for 2.25x+3(6)=11/5x-18 equation:

2.25x+3(6)=11/5x-18

We move all terms to the left:

2.25x+3(6)-(11/5x-18)=0


Domain of the equation: 5x-18)!=0

x∈R


We get rid of parentheses

2.25x-11/5x+18+36=0

We multiply all the terms by the denominator


(2.25x)*5x+18*5x+36*5x-11=0

We add all the numbers together, and all the variables

(+2.25x)*5x+18*5x+36*5x-11=0

We multiply parentheses

10x^2+18*5x+36*5x-11=0

Wy multiply elements

10x^2+90x+180x-11=0

We add all the numbers together, and all the variables

10x^2+270x-11=0

a = 10; b = 270; c = -11;
Δ = b2-4ac
Δ = 2702-4·10·(-11)
Δ = 73340
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:

$\sqrt{\Delta}=\sqrt{73340}=\sqrt{4*18335}=\sqrt{4}*\sqrt{18335}=2\sqrt{18335}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-2\sqrt{18335}}{2*10}=\frac{-270-2\sqrt{18335}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+2\sqrt{18335}}{2*10}=\frac{-270+2\sqrt{18335}}{20}
$