5x(8x+12)=26

Solution for 5x(8x+12)=26 equation:

5x(8x+12)=26

We move all terms to the left:

5x(8x+12)-(26)=0

We multiply parentheses

40x^2+60x-26=0

a = 40; b = 60; c = -26;
Δ = b2-4ac
Δ = 602-4·40·(-26)
Δ = 7760
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:

$\sqrt{\Delta}=\sqrt{7760}=\sqrt{16*485}=\sqrt{16}*\sqrt{485}=4\sqrt{485}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{485}}{2*40}=\frac{-60-4\sqrt{485}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{485}}{2*40}=\frac{-60+4\sqrt{485}}{80}
$