(10x+7)(12x+22)=45

Solution for (10x+7)(12x+22)=45 equation:

(10x+7)(12x+22)=45

We move all terms to the left:

(10x+7)(12x+22)-(45)=0

We multiply parentheses ..

(+120x^2+220x+84x+154)-45=0

We get rid of parentheses

120x^2+220x+84x+154-45=0

We add all the numbers together, and all the variables

120x^2+304x+109=0

a = 120; b = 304; c = +109;
Δ = b2-4ac
Δ = 3042-4·120·109
Δ = 40096
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:

$\sqrt{\Delta}=\sqrt{40096}=\sqrt{16*2506}=\sqrt{16}*\sqrt{2506}=4\sqrt{2506}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(304)-4\sqrt{2506}}{2*120}=\frac{-304-4\sqrt{2506}}{240}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(304)+4\sqrt{2506}}{2*120}=\frac{-304+4\sqrt{2506}}{240}
$