(4x)(7x+2)=7

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

(4x)(7x+2)=7

We move all terms to the left:

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

We multiply parentheses

28x^2+8x-7=0

a = 28; b = 8; c = -7;
Δ = b2-4ac
Δ = 82-4·28·(-7)
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{-(8)-4\sqrt{53}}{2*28}=\frac{-8-4\sqrt{53}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{53}}{2*28}=\frac{-8+4\sqrt{53}}{56}
$