(3x+10)(6x-14)=180

Solution for (3x+10)(6x-14)=180 equation:

(3x+10)(6x-14)=180

We move all terms to the left:

(3x+10)(6x-14)-(180)=0

We multiply parentheses ..

(+18x^2-42x+60x-140)-180=0

We get rid of parentheses

18x^2-42x+60x-140-180=0

We add all the numbers together, and all the variables

18x^2+18x-320=0

a = 18; b = 18; c = -320;
Δ = b2-4ac
Δ = 182-4·18·(-320)
Δ = 23364
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:

$\sqrt{\Delta}=\sqrt{23364}=\sqrt{36*649}=\sqrt{36}*\sqrt{649}=6\sqrt{649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{649}}{2*18}=\frac{-18-6\sqrt{649}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{649}}{2*18}=\frac{-18+6\sqrt{649}}{36}
$