(x+2)(x-7)=10(x+7)

Solution for (x+2)(x-7)=10(x+7) equation:

(x+2)(x-7)=10(x+7)

We move all terms to the left:

(x+2)(x-7)-(10(x+7))=0

We multiply parentheses ..

(+x^2-7x+2x-14)-(10(x+7))=0


We calculate terms in parentheses: -(10(x+7)), so:

10(x+7)

We multiply parentheses

10x+70

Back to the equation:

-(10x+70)


We get rid of parentheses

x^2-7x+2x-10x-14-70=0

We add all the numbers together, and all the variables

x^2-15x-84=0

a = 1; b = -15; c = -84;
Δ = b2-4ac
Δ = -152-4·1·(-84)
Δ = 561
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{-(-15)-\sqrt{561}}{2*1}=\frac{15-\sqrt{561}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{561}}{2*1}=\frac{15+\sqrt{561}}{2}
$