(2x-1)(x+10)=-34

Solution for (2x-1)(x+10)=-34 equation:

(2x-1)(x+10)=-34

We move all terms to the left:

(2x-1)(x+10)-(-34)=0

We add all the numbers together, and all the variables

(2x-1)(x+10)+34=0

We multiply parentheses ..

(+2x^2+20x-1x-10)+34=0

We get rid of parentheses

2x^2+20x-1x-10+34=0

We add all the numbers together, and all the variables

2x^2+19x+24=0

a = 2; b = 19; c = +24;
Δ = b2-4ac
Δ = 192-4·2·24
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-13}{2*2}=\frac{-32}{4}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+13}{2*2}=\frac{-6}{4}
=-1+1/2
$