12x+13=5(45x+2)12x+13=5(45x+2)

Solution for 12x+13=5(45x+2)12x+13=5(45x+2) equation:

12x+13=5(45x+2)12x+13=5(45x+2)

We move all terms to the left:

12x+13-(5(45x+2)12x+13)=0


We calculate terms in parentheses: -(5(45x+2)12x+13), so:

5(45x+2)12x+13

We multiply parentheses

2700x^2+120x+13

Back to the equation:

-(2700x^2+120x+13)


We get rid of parentheses

-2700x^2+12x-120x-13+13=0

We add all the numbers together, and all the variables

-2700x^2-108x=0

a = -2700; b = -108; c = 0;
Δ = b2-4ac
Δ = -1082-4·(-2700)·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-108}{2*-2700}=\frac{0}{-5400}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+108}{2*-2700}=\frac{216}{-5400}
=-1/25
$