7=8x(4x+3)

Solution for 7=8x(4x+3) equation:

7=8x(4x+3)

We move all terms to the left:

7-(8x(4x+3))=0


We calculate terms in parentheses: -(8x(4x+3)), so:

8x(4x+3)

We multiply parentheses

32x^2+24x

Back to the equation:

-(32x^2+24x)


We get rid of parentheses

-32x^2-24x+7=0

a = -32; b = -24; c = +7;
Δ = b2-4ac
Δ = -242-4·(-32)·7
Δ = 1472
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:

$\sqrt{\Delta}=\sqrt{1472}=\sqrt{64*23}=\sqrt{64}*\sqrt{23}=8\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{23}}{2*-32}=\frac{24-8\sqrt{23}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{23}}{2*-32}=\frac{24+8\sqrt{23}}{-64}
$