(3x+5)(4x+6)=6

Solution for (3x+5)(4x+6)=6 equation:

(3x+5)(4x+6)=6

We move all terms to the left:

(3x+5)(4x+6)-(6)=0

We multiply parentheses ..

(+12x^2+18x+20x+30)-6=0

We get rid of parentheses

12x^2+18x+20x+30-6=0

We add all the numbers together, and all the variables

12x^2+38x+24=0

a = 12; b = 38; c = +24;
Δ = b2-4ac
Δ = 382-4·12·24
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{73}}{2*12}=\frac{-38-2\sqrt{73}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{73}}{2*12}=\frac{-38+2\sqrt{73}}{24}
$