(4x+4)(2x+9)=53

Solution for (4x+4)(2x+9)=53 equation:

(4x+4)(2x+9)=53

We move all terms to the left:

(4x+4)(2x+9)-(53)=0

We multiply parentheses ..

(+8x^2+36x+8x+36)-53=0

We get rid of parentheses

8x^2+36x+8x+36-53=0

We add all the numbers together, and all the variables

8x^2+44x-17=0

a = 8; b = 44; c = -17;
Δ = b2-4ac
Δ = 442-4·8·(-17)
Δ = 2480
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:

$\sqrt{\Delta}=\sqrt{2480}=\sqrt{16*155}=\sqrt{16}*\sqrt{155}=4\sqrt{155}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{155}}{2*8}=\frac{-44-4\sqrt{155}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{155}}{2*8}=\frac{-44+4\sqrt{155}}{16}
$