10x(x+7)=82

Solution for 10x(x+7)=82 equation:

10x(x+7)=82

We move all terms to the left:

10x(x+7)-(82)=0

We multiply parentheses

10x^2+70x-82=0

a = 10; b = 70; c = -82;
Δ = b2-4ac
Δ = 702-4·10·(-82)
Δ = 8180
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:

$\sqrt{\Delta}=\sqrt{8180}=\sqrt{4*2045}=\sqrt{4}*\sqrt{2045}=2\sqrt{2045}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{2045}}{2*10}=\frac{-70-2\sqrt{2045}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{2045}}{2*10}=\frac{-70+2\sqrt{2045}}{20}
$