(4x+13)(6x+2)=(14x-13)

Solution for (4x+13)(6x+2)=(14x-13) equation:

(4x+13)(6x+2)=(14x-13)

We move all terms to the left:

(4x+13)(6x+2)-((14x-13))=0

We multiply parentheses ..

(+24x^2+8x+78x+26)-((14x-13))=0


We calculate terms in parentheses: -((14x-13)), so:

(14x-13)

We get rid of parentheses

14x-13

Back to the equation:

-(14x-13)


We get rid of parentheses

24x^2+8x+78x-14x+26+13=0

We add all the numbers together, and all the variables

24x^2+72x+39=0

a = 24; b = 72; c = +39;
Δ = b2-4ac
Δ = 722-4·24·39
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{10}}{2*24}=\frac{-72-12\sqrt{10}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{10}}{2*24}=\frac{-72+12\sqrt{10}}{48}
$