2x(4x-7)=29

Solution for 2x(4x-7)=29 equation:

2x(4x-7)=29

We move all terms to the left:

2x(4x-7)-(29)=0

We multiply parentheses

8x^2-14x-29=0

a = 8; b = -14; c = -29;
Δ = b2-4ac
Δ = -142-4·8·(-29)
Δ = 1124
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:

$\sqrt{\Delta}=\sqrt{1124}=\sqrt{4*281}=\sqrt{4}*\sqrt{281}=2\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{281}}{2*8}=\frac{14-2\sqrt{281}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{281}}{2*8}=\frac{14+2\sqrt{281}}{16}
$