(12x-3)(5x+12)=(3x+13)

Solution for (12x-3)(5x+12)=(3x+13) equation:

(12x-3)(5x+12)=(3x+13)

We move all terms to the left:

(12x-3)(5x+12)-((3x+13))=0

We multiply parentheses ..

(+60x^2+144x-15x-36)-((3x+13))=0


We calculate terms in parentheses: -((3x+13)), so:

(3x+13)

We get rid of parentheses

3x+13

Back to the equation:

-(3x+13)


We get rid of parentheses

60x^2+144x-15x-3x-36-13=0

We add all the numbers together, and all the variables

60x^2+126x-49=0

a = 60; b = 126; c = -49;
Δ = b2-4ac
Δ = 1262-4·60·(-49)
Δ = 27636
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:

$\sqrt{\Delta}=\sqrt{27636}=\sqrt{196*141}=\sqrt{196}*\sqrt{141}=14\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-14\sqrt{141}}{2*60}=\frac{-126-14\sqrt{141}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+14\sqrt{141}}{2*60}=\frac{-126+14\sqrt{141}}{120}
$