5(x+7)-2(x-4)x=2

Solution for 5(x+7)-2(x-4)x=2 equation:

5(x+7)-2(x-4)x=2

We move all terms to the left:

5(x+7)-2(x-4)x-(2)=0

We multiply parentheses

-2x^2+5x+8x+35-2=0

We add all the numbers together, and all the variables

-2x^2+13x+33=0

a = -2; b = 13; c = +33;
Δ = b2-4ac
Δ = 132-4·(-2)·33
Δ = 433
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{433}}{2*-2}=\frac{-13-\sqrt{433}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{433}}{2*-2}=\frac{-13+\sqrt{433}}{-4}
$