(6x+7)(13x+21)=180

Solution for (6x+7)(13x+21)=180 equation:

(6x+7)(13x+21)=180

We move all terms to the left:

(6x+7)(13x+21)-(180)=0

We multiply parentheses ..

(+78x^2+126x+91x+147)-180=0

We get rid of parentheses

78x^2+126x+91x+147-180=0

We add all the numbers together, and all the variables

78x^2+217x-33=0

a = 78; b = 217; c = -33;
Δ = b2-4ac
Δ = 2172-4·78·(-33)
Δ = 57385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(217)-\sqrt{57385}}{2*78}=\frac{-217-\sqrt{57385}}{156}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(217)+\sqrt{57385}}{2*78}=\frac{-217+\sqrt{57385}}{156}
$