10.1x+3(6)=11/5x-18

Solution for 10.1x+3(6)=11/5x-18 equation:

10.1x+3(6)=11/5x-18

We move all terms to the left:

10.1x+3(6)-(11/5x-18)=0


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

x∈R


We get rid of parentheses

10.1x-11/5x+18+36=0

We multiply all the terms by the denominator


(10.1x)*5x+18*5x+36*5x-11=0

We add all the numbers together, and all the variables

(+10.1x)*5x+18*5x+36*5x-11=0

We multiply parentheses

50x^2+18*5x+36*5x-11=0

Wy multiply elements

50x^2+90x+180x-11=0

We add all the numbers together, and all the variables

50x^2+270x-11=0

a = 50; b = 270; c = -11;
Δ = b2-4ac
Δ = 2702-4·50·(-11)
Δ = 75100
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:

$\sqrt{\Delta}=\sqrt{75100}=\sqrt{100*751}=\sqrt{100}*\sqrt{751}=10\sqrt{751}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-10\sqrt{751}}{2*50}=\frac{-270-10\sqrt{751}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+10\sqrt{751}}{2*50}=\frac{-270+10\sqrt{751}}{100}
$