4x(2x-5)=14

Solution for 4x(2x-5)=14 equation:

4x(2x-5)=14

We move all terms to the left:

4x(2x-5)-(14)=0

We multiply parentheses

8x^2-20x-14=0

a = 8; b = -20; c = -14;
Δ = b2-4ac
Δ = -202-4·8·(-14)
Δ = 848
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:

$\sqrt{\Delta}=\sqrt{848}=\sqrt{16*53}=\sqrt{16}*\sqrt{53}=4\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{53}}{2*8}=\frac{20-4\sqrt{53}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{53}}{2*8}=\frac{20+4\sqrt{53}}{16}
$