4x(2x+3)-7=53

Solution for 4x(2x+3)-7=53 equation:

4x(2x+3)-7=53

We move all terms to the left:

4x(2x+3)-7-(53)=0

We add all the numbers together, and all the variables

4x(2x+3)-60=0

We multiply parentheses

8x^2+12x-60=0

a = 8; b = 12; c = -60;
Δ = b2-4ac
Δ = 122-4·8·(-60)
Δ = 2064
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:

$\sqrt{\Delta}=\sqrt{2064}=\sqrt{16*129}=\sqrt{16}*\sqrt{129}=4\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{129}}{2*8}=\frac{-12-4\sqrt{129}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{129}}{2*8}=\frac{-12+4\sqrt{129}}{16}
$