7x(4x-2)=10

Solution for 7x(4x-2)=10 equation:

7x(4x-2)=10

We move all terms to the left:

7x(4x-2)-(10)=0

We multiply parentheses

28x^2-14x-10=0

a = 28; b = -14; c = -10;
Δ = b2-4ac
Δ = -142-4·28·(-10)
Δ = 1316
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:

$\sqrt{\Delta}=\sqrt{1316}=\sqrt{4*329}=\sqrt{4}*\sqrt{329}=2\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{329}}{2*28}=\frac{14-2\sqrt{329}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{329}}{2*28}=\frac{14+2\sqrt{329}}{56}
$