-10x(x+5)+74=-13-3

Solution for -10x(x+5)+74=-13-3 equation:

-10x(x+5)+74=-13-3

We move all terms to the left:

-10x(x+5)+74-(-13-3)=0

We add all the numbers together, and all the variables

-10x(x+5)+74-(-16)=0

We add all the numbers together, and all the variables

-10x(x+5)+90=0

We multiply parentheses

-10x^2-50x+90=0

a = -10; b = -50; c = +90;
Δ = b2-4ac
Δ = -502-4·(-10)·90
Δ = 6100
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:

$\sqrt{\Delta}=\sqrt{6100}=\sqrt{100*61}=\sqrt{100}*\sqrt{61}=10\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{61}}{2*-10}=\frac{50-10\sqrt{61}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{61}}{2*-10}=\frac{50+10\sqrt{61}}{-20}
$