(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 get rid of parentheses

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

We multiply parentheses ..

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

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+4x-29=0

a = 8; b = 4; c = -29;
Δ = b2-4ac
Δ = 42-4·8·(-29)
Δ = 944
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:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{59}}{2*8}=\frac{-4-4\sqrt{59}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{59}}{2*8}=\frac{-4+4\sqrt{59}}{16}
$