(2x+7)(4x-7)=18

Solution for (2x+7)(4x-7)=18 equation:

(2x+7)(4x-7)=18

We move all terms to the left:

(2x+7)(4x-7)-(18)=0

We multiply parentheses ..

(+8x^2-14x+28x-49)-18=0

We get rid of parentheses

8x^2-14x+28x-49-18=0

We add all the numbers together, and all the variables

8x^2+14x-67=0

a = 8; b = 14; c = -67;
Δ = b2-4ac
Δ = 142-4·8·(-67)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{65}}{2*8}=\frac{-14-6\sqrt{65}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{65}}{2*8}=\frac{-14+6\sqrt{65}}{16}
$