5x*(2x-10)=34

Solution for 5x*(2x-10)=34 equation:

5x*(2x-10)=34

We move all terms to the left:

5x*(2x-10)-(34)=0

We multiply parentheses

10x^2-50x-34=0

a = 10; b = -50; c = -34;
Δ = b2-4ac
Δ = -502-4·10·(-34)
Δ = 3860
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:

$\sqrt{\Delta}=\sqrt{3860}=\sqrt{4*965}=\sqrt{4}*\sqrt{965}=2\sqrt{965}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{965}}{2*10}=\frac{50-2\sqrt{965}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{965}}{2*10}=\frac{50+2\sqrt{965}}{20}
$