(7x+10)(8x+20)=180

Solution for (7x+10)(8x+20)=180 equation:

(7x+10)(8x+20)=180

We move all terms to the left:

(7x+10)(8x+20)-(180)=0

We multiply parentheses ..

(+56x^2+140x+80x+200)-180=0

We get rid of parentheses

56x^2+140x+80x+200-180=0

We add all the numbers together, and all the variables

56x^2+220x+20=0

a = 56; b = 220; c = +20;
Δ = b2-4ac
Δ = 2202-4·56·20
Δ = 43920
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:

$\sqrt{\Delta}=\sqrt{43920}=\sqrt{144*305}=\sqrt{144}*\sqrt{305}=12\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(220)-12\sqrt{305}}{2*56}=\frac{-220-12\sqrt{305}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(220)+12\sqrt{305}}{2*56}=\frac{-220+12\sqrt{305}}{112}
$