17x(x+3)=136

Solution for 17x(x+3)=136 equation:

17x(x+3)=136

We move all terms to the left:

17x(x+3)-(136)=0

We multiply parentheses

17x^2+51x-136=0

a = 17; b = 51; c = -136;
Δ = b2-4ac
Δ = 512-4·17·(-136)
Δ = 11849
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:

$\sqrt{\Delta}=\sqrt{11849}=\sqrt{289*41}=\sqrt{289}*\sqrt{41}=17\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-17\sqrt{41}}{2*17}=\frac{-51-17\sqrt{41}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+17\sqrt{41}}{2*17}=\frac{-51+17\sqrt{41}}{34}
$