6(24)=x(x+7)

Solution for 6(24)=x(x+7) equation:

6(24)=x(x+7)

We move all terms to the left:

6(24)-(x(x+7))=0


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

x(x+7)

We multiply parentheses

x^2+7x

Back to the equation:

-(x^2+7x)


We get rid of parentheses

-x^2-7x+624=0

We add all the numbers together, and all the variables

-1x^2-7x+624=0

a = -1; b = -7; c = +624;
Δ = b2-4ac
Δ = -72-4·(-1)·624
Δ = 2545
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{2545}}{2*-1}=\frac{7-\sqrt{2545}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{2545}}{2*-1}=\frac{7+\sqrt{2545}}{-2}
$