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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

16x^2-56x+10=0

a = 16; b = -56; c = +10;
Δ = b2-4ac
Δ = -562-4·16·10
Δ = 2496
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:

$\sqrt{\Delta}=\sqrt{2496}=\sqrt{64*39}=\sqrt{64}*\sqrt{39}=8\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{39}}{2*16}=\frac{56-8\sqrt{39}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{39}}{2*16}=\frac{56+8\sqrt{39}}{32}
$