5x-3(x-4)+2x(x-5)=30

Solution for 5x-3(x-4)+2x(x-5)=30 equation:

5x-3(x-4)+2x(x-5)=30

We move all terms to the left:

5x-3(x-4)+2x(x-5)-(30)=0

We multiply parentheses

2x^2+5x-3x-10x+12-30=0

We add all the numbers together, and all the variables

2x^2-8x-18=0

a = 2; b = -8; c = -18;
Δ = b2-4ac
Δ = -82-4·2·(-18)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{13}}{2*2}=\frac{8-4\sqrt{13}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{13}}{2*2}=\frac{8+4\sqrt{13}}{4}
$