(2x+27)(2x-11)=100

Solution for (2x+27)(2x-11)=100 equation:

(2x+27)(2x-11)=100

We move all terms to the left:

(2x+27)(2x-11)-(100)=0

We multiply parentheses ..

(+4x^2-22x+54x-297)-100=0

We get rid of parentheses

4x^2-22x+54x-297-100=0

We add all the numbers together, and all the variables

4x^2+32x-397=0

a = 4; b = 32; c = -397;
Δ = b2-4ac
Δ = 322-4·4·(-397)
Δ = 7376
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:

$\sqrt{\Delta}=\sqrt{7376}=\sqrt{16*461}=\sqrt{16}*\sqrt{461}=4\sqrt{461}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{461}}{2*4}=\frac{-32-4\sqrt{461}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{461}}{2*4}=\frac{-32+4\sqrt{461}}{8}
$