60x+5x(22-x)-225+30x=8

Solution for 60x+5x(22-x)-225+30x=8 equation:

60x+5x(22-x)-225+30x=8

We move all terms to the left:

60x+5x(22-x)-225+30x-(8)=0

We add all the numbers together, and all the variables

60x+5x(-1x+22)+30x-225-8=0

We add all the numbers together, and all the variables

90x+5x(-1x+22)-233=0

We multiply parentheses

-5x^2+90x+110x-233=0

We add all the numbers together, and all the variables

-5x^2+200x-233=0

a = -5; b = 200; c = -233;
Δ = b2-4ac
Δ = 2002-4·(-5)·(-233)
Δ = 35340
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:

$\sqrt{\Delta}=\sqrt{35340}=\sqrt{4*8835}=\sqrt{4}*\sqrt{8835}=2\sqrt{8835}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-2\sqrt{8835}}{2*-5}=\frac{-200-2\sqrt{8835}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+2\sqrt{8835}}{2*-5}=\frac{-200+2\sqrt{8835}}{-10}
$