(x+5)(x+7)=70

Solution for (x+5)(x+7)=70 equation:

(x+5)(x+7)=70

We move all terms to the left:

(x+5)(x+7)-(70)=0

We multiply parentheses ..

(+x^2+7x+5x+35)-70=0

We get rid of parentheses

x^2+7x+5x+35-70=0

We add all the numbers together, and all the variables

x^2+12x-35=0

a = 1; b = 12; c = -35;
Δ = b2-4ac
Δ = 122-4·1·(-35)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{71}}{2*1}=\frac{-12-2\sqrt{71}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{71}}{2*1}=\frac{-12+2\sqrt{71}}{2}
$