-2x(5x+5)-3x+4=-34

Solution for -2x(5x+5)-3x+4=-34 equation:

-2x(5x+5)-3x+4=-34

We move all terms to the left:

-2x(5x+5)-3x+4-(-34)=0

We add all the numbers together, and all the variables

-3x-2x(5x+5)+38=0

We multiply parentheses

-10x^2-3x-10x+38=0

We add all the numbers together, and all the variables

-10x^2-13x+38=0

a = -10; b = -13; c = +38;
Δ = b2-4ac
Δ = -132-4·(-10)·38
Δ = 1689
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{-(-13)-\sqrt{1689}}{2*-10}=\frac{13-\sqrt{1689}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{1689}}{2*-10}=\frac{13+\sqrt{1689}}{-20}
$