(6x+4)(7x+4)=60

Solution for (6x+4)(7x+4)=60 equation:

(6x+4)(7x+4)=60

We move all terms to the left:

(6x+4)(7x+4)-(60)=0

We multiply parentheses ..

(+42x^2+24x+28x+16)-60=0

We get rid of parentheses

42x^2+24x+28x+16-60=0

We add all the numbers together, and all the variables

42x^2+52x-44=0

a = 42; b = 52; c = -44;
Δ = b2-4ac
Δ = 522-4·42·(-44)
Δ = 10096
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:

$\sqrt{\Delta}=\sqrt{10096}=\sqrt{16*631}=\sqrt{16}*\sqrt{631}=4\sqrt{631}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{631}}{2*42}=\frac{-52-4\sqrt{631}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{631}}{2*42}=\frac{-52+4\sqrt{631}}{84}
$