(2x+10)(4x+1)=180

Solution for (2x+10)(4x+1)=180 equation:

(2x+10)(4x+1)=180

We move all terms to the left:

(2x+10)(4x+1)-(180)=0

We multiply parentheses ..

(+8x^2+2x+40x+10)-180=0

We get rid of parentheses

8x^2+2x+40x+10-180=0

We add all the numbers together, and all the variables

8x^2+42x-170=0

a = 8; b = 42; c = -170;
Δ = b2-4ac
Δ = 422-4·8·(-170)
Δ = 7204
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:

$\sqrt{\Delta}=\sqrt{7204}=\sqrt{4*1801}=\sqrt{4}*\sqrt{1801}=2\sqrt{1801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{1801}}{2*8}=\frac{-42-2\sqrt{1801}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{1801}}{2*8}=\frac{-42+2\sqrt{1801}}{16}
$