18(18+24)=(x+7)(x+7)

Solution for 18(18+24)=(x+7)(x+7) equation:

18(18+24)=(x+7)(x+7)

We move all terms to the left:

18(18+24)-((x+7)(x+7))=0

We add all the numbers together, and all the variables

-((x+7)(x+7))+1842=0

We multiply parentheses ..

-((+x^2+7x+7x+49))+1842=0


We calculate terms in parentheses: -((+x^2+7x+7x+49)), so:

(+x^2+7x+7x+49)

We get rid of parentheses

x^2+7x+7x+49

We add all the numbers together, and all the variables

x^2+14x+49

Back to the equation:

-(x^2+14x+49)


We get rid of parentheses

-x^2-14x-49+1842=0

We add all the numbers together, and all the variables

-1x^2-14x+1793=0

a = -1; b = -14; c = +1793;
Δ = b2-4ac
Δ = -142-4·(-1)·1793
Δ = 7368
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:

$\sqrt{\Delta}=\sqrt{7368}=\sqrt{4*1842}=\sqrt{4}*\sqrt{1842}=2\sqrt{1842}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{1842}}{2*-1}=\frac{14-2\sqrt{1842}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{1842}}{2*-1}=\frac{14+2\sqrt{1842}}{-2}
$