3x(11x-7)=13x+25

Solution for 3x(11x-7)=13x+25 equation:

3x(11x-7)=13x+25

We move all terms to the left:

3x(11x-7)-(13x+25)=0

We multiply parentheses

33x^2-21x-(13x+25)=0

We get rid of parentheses

33x^2-21x-13x-25=0

We add all the numbers together, and all the variables

33x^2-34x-25=0

a = 33; b = -34; c = -25;
Δ = b2-4ac
Δ = -342-4·33·(-25)
Δ = 4456
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:

$\sqrt{\Delta}=\sqrt{4456}=\sqrt{4*1114}=\sqrt{4}*\sqrt{1114}=2\sqrt{1114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{1114}}{2*33}=\frac{34-2\sqrt{1114}}{66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{1114}}{2*33}=\frac{34+2\sqrt{1114}}{66}
$