(4x-14)(2x+7)=180

Solution for (4x-14)(2x+7)=180 equation:

(4x-14)(2x+7)=180

We move all terms to the left:

(4x-14)(2x+7)-(180)=0

We multiply parentheses ..

(+8x^2+28x-28x-98)-180=0

We get rid of parentheses

8x^2+28x-28x-98-180=0

We add all the numbers together, and all the variables

8x^2-278=0

a = 8; b = 0; c = -278;
Δ = b2-4ac
Δ = 02-4·8·(-278)
Δ = 8896
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:

$\sqrt{\Delta}=\sqrt{8896}=\sqrt{64*139}=\sqrt{64}*\sqrt{139}=8\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{139}}{2*8}=\frac{0-8\sqrt{139}}{16}
=-\frac{8\sqrt{139}}{16}
=-\frac{\sqrt{139}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{139}}{2*8}=\frac{0+8\sqrt{139}}{16}
=\frac{8\sqrt{139}}{16}
=\frac{\sqrt{139}}{2}
$