59=6x(3x+4)

Solution for 59=6x(3x+4) equation:

59=6x(3x+4)

We move all terms to the left:

59-(6x(3x+4))=0


We calculate terms in parentheses: -(6x(3x+4)), so:

6x(3x+4)

We multiply parentheses

18x^2+24x

Back to the equation:

-(18x^2+24x)


We get rid of parentheses

-18x^2-24x+59=0

a = -18; b = -24; c = +59;
Δ = b2-4ac
Δ = -242-4·(-18)·59
Δ = 4824
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:

$\sqrt{\Delta}=\sqrt{4824}=\sqrt{36*134}=\sqrt{36}*\sqrt{134}=6\sqrt{134}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{134}}{2*-18}=\frac{24-6\sqrt{134}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{134}}{2*-18}=\frac{24+6\sqrt{134}}{-36}
$