58=(5x+10)(30-2x)

Solution for 58=(5x+10)(30-2x) equation:

58=(5x+10)(30-2x)

We move all terms to the left:

58-((5x+10)(30-2x))=0

We add all the numbers together, and all the variables

-((5x+10)(-2x+30))+58=0

We multiply parentheses ..

-((-10x^2+150x-20x+300))+58=0


We calculate terms in parentheses: -((-10x^2+150x-20x+300)), so:

(-10x^2+150x-20x+300)

We get rid of parentheses

-10x^2+150x-20x+300

We add all the numbers together, and all the variables

-10x^2+130x+300

Back to the equation:

-(-10x^2+130x+300)


We get rid of parentheses

10x^2-130x-300+58=0

We add all the numbers together, and all the variables

10x^2-130x-242=0

a = 10; b = -130; c = -242;
Δ = b2-4ac
Δ = -1302-4·10·(-242)
Δ = 26580
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:

$\sqrt{\Delta}=\sqrt{26580}=\sqrt{4*6645}=\sqrt{4}*\sqrt{6645}=2\sqrt{6645}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{6645}}{2*10}=\frac{130-2\sqrt{6645}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{6645}}{2*10}=\frac{130+2\sqrt{6645}}{20}
$