(2x+6)(4x+7)=(6x+13)

Solution for (2x+6)(4x+7)=(6x+13) equation:

(2x+6)(4x+7)=(6x+13)

We move all terms to the left:

(2x+6)(4x+7)-((6x+13))=0

We multiply parentheses ..

(+8x^2+14x+24x+42)-((6x+13))=0


We calculate terms in parentheses: -((6x+13)), so:

(6x+13)

We get rid of parentheses

6x+13

Back to the equation:

-(6x+13)


We get rid of parentheses

8x^2+14x+24x-6x+42-13=0

We add all the numbers together, and all the variables

8x^2+32x+29=0

a = 8; b = 32; c = +29;
Δ = b2-4ac
Δ = 322-4·8·29
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{6}}{2*8}=\frac{-32-4\sqrt{6}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{6}}{2*8}=\frac{-32+4\sqrt{6}}{16}
$