(14x+6)(10x+6)=180

Solution for (14x+6)(10x+6)=180 equation:

(14x+6)(10x+6)=180

We move all terms to the left:

(14x+6)(10x+6)-(180)=0

We multiply parentheses ..

(+140x^2+84x+60x+36)-180=0

We get rid of parentheses

140x^2+84x+60x+36-180=0

We add all the numbers together, and all the variables

140x^2+144x-144=0

a = 140; b = 144; c = -144;
Δ = b2-4ac
Δ = 1442-4·140·(-144)
Δ = 101376
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:

$\sqrt{\Delta}=\sqrt{101376}=\sqrt{9216*11}=\sqrt{9216}*\sqrt{11}=96\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-96\sqrt{11}}{2*140}=\frac{-144-96\sqrt{11}}{280}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+96\sqrt{11}}{2*140}=\frac{-144+96\sqrt{11}}{280}
$