2x(5-3+x)-3x+4(5)=83

Solution for 2x(5-3+x)-3x+4(5)=83 equation:

2x(5-3+x)-3x+4(5)=83

We move all terms to the left:

2x(5-3+x)-3x+4(5)-(83)=0

We add all the numbers together, and all the variables

2x(x+2)-3x+45-83=0

We add all the numbers together, and all the variables

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

We multiply parentheses

2x^2-3x+4x-38=0

We add all the numbers together, and all the variables

2x^2+x-38=0

a = 2; b = 1; c = -38;
Δ = b2-4ac
Δ = 12-4·2·(-38)
Δ = 305
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{-(1)-\sqrt{305}}{2*2}=\frac{-1-\sqrt{305}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{305}}{2*2}=\frac{-1+\sqrt{305}}{4}
$