3(10)(24)=(10+x)(24+x)

Solution for 3(10)(24)=(10+x)(24+x) equation:

3(10)(24)=(10+x)(24+x)

We move all terms to the left:

3(10)(24)-((10+x)(24+x))=0

We add all the numbers together, and all the variables

-((x+10)(x+24))+31024=0

We multiply parentheses ..

-((+x^2+24x+10x+240))+31024=0


We calculate terms in parentheses: -((+x^2+24x+10x+240)), so:

(+x^2+24x+10x+240)

We get rid of parentheses

x^2+24x+10x+240

We add all the numbers together, and all the variables

x^2+34x+240

Back to the equation:

-(x^2+34x+240)


We get rid of parentheses

-x^2-34x-240+31024=0

We add all the numbers together, and all the variables

-1x^2-34x+30784=0

a = -1; b = -34; c = +30784;
Δ = b2-4ac
Δ = -342-4·(-1)·30784
Δ = 124292
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:

$\sqrt{\Delta}=\sqrt{124292}=\sqrt{4*31073}=\sqrt{4}*\sqrt{31073}=2\sqrt{31073}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{31073}}{2*-1}=\frac{34-2\sqrt{31073}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{31073}}{2*-1}=\frac{34+2\sqrt{31073}}{-2}
$