x(x+7)-3(x+5)=-10(x+6)

Solution for x(x+7)-3(x+5)=-10(x+6) equation:

x(x+7)-3(x+5)=-10(x+6)

We move all terms to the left:

x(x+7)-3(x+5)-(-10(x+6))=0

We multiply parentheses

x^2+7x-3x-(-10(x+6))-15=0


We calculate terms in parentheses: -(-10(x+6)), so:

-10(x+6)

We multiply parentheses

-10x-60

Back to the equation:

-(-10x-60)


We add all the numbers together, and all the variables

x^2+4x-(-10x-60)-15=0

We get rid of parentheses

x^2+4x+10x+60-15=0

We add all the numbers together, and all the variables

x^2+14x+45=0

a = 1; b = 14; c = +45;
Δ = b2-4ac
Δ = 142-4·1·45
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4}{2*1}=\frac{-10}{2}
=-5
$