-15x(x-2)=-34

Solution for -15x(x-2)=-34 equation:

-15x(x-2)=-34

We move all terms to the left:

-15x(x-2)-(-34)=0

We add all the numbers together, and all the variables

-15x(x-2)+34=0

We multiply parentheses

-15x^2+30x+34=0

a = -15; b = 30; c = +34;
Δ = b2-4ac
Δ = 302-4·(-15)·34
Δ = 2940
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:

$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-14\sqrt{15}}{2*-15}=\frac{-30-14\sqrt{15}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+14\sqrt{15}}{2*-15}=\frac{-30+14\sqrt{15}}{-30}
$