5(2x+5)4x=7

Solution for 5(2x+5)4x=7 equation:

5(2x+5)4x=7

We move all terms to the left:

5(2x+5)4x-(7)=0

We multiply parentheses

40x^2+100x-7=0

a = 40; b = 100; c = -7;
Δ = b2-4ac
Δ = 1002-4·40·(-7)
Δ = 11120
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:

$\sqrt{\Delta}=\sqrt{11120}=\sqrt{16*695}=\sqrt{16}*\sqrt{695}=4\sqrt{695}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{695}}{2*40}=\frac{-100-4\sqrt{695}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{695}}{2*40}=\frac{-100+4\sqrt{695}}{80}
$