-10x(x+13)+14x=62

Solution for -10x(x+13)+14x=62 equation:

-10x(x+13)+14x=62

We move all terms to the left:

-10x(x+13)+14x-(62)=0

We add all the numbers together, and all the variables

14x-10x(x+13)-62=0

We multiply parentheses

-10x^2+14x-130x-62=0

We add all the numbers together, and all the variables

-10x^2-116x-62=0

a = -10; b = -116; c = -62;
Δ = b2-4ac
Δ = -1162-4·(-10)·(-62)
Δ = 10976
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:

$\sqrt{\Delta}=\sqrt{10976}=\sqrt{784*14}=\sqrt{784}*\sqrt{14}=28\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-28\sqrt{14}}{2*-10}=\frac{116-28\sqrt{14}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+28\sqrt{14}}{2*-10}=\frac{116+28\sqrt{14}}{-20}
$