6*5=x(7+x)

Solution for 6*5=x(7+x) equation:

6*5=x(7+x)

We move all terms to the left:

6*5-(x(7+x))=0

We add all the numbers together, and all the variables

-(x(x+7))+6*5=0

We add all the numbers together, and all the variables

-(x(x+7))+30=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+30=0

We add all the numbers together, and all the variables

-1x^2-7x+30=0

a = -1; b = -7; c = +30;
Δ = b2-4ac
Δ = -72-4·(-1)·30
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*-1}=\frac{-6}{-2}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*-1}=\frac{20}{-2}
=-10
$