4-2x(3-x)+5x-7=12x-19

Solution for 4-2x(3-x)+5x-7=12x-19 equation:

4-2x(3-x)+5x-7=12x-19

We move all terms to the left:

4-2x(3-x)+5x-7-(12x-19)=0

We add all the numbers together, and all the variables

-2x(-1x+3)+5x-(12x-19)+4-7=0

We add all the numbers together, and all the variables

5x-2x(-1x+3)-(12x-19)-3=0

We multiply parentheses

2x^2+5x-6x-(12x-19)-3=0

We get rid of parentheses

2x^2+5x-6x-12x+19-3=0

We add all the numbers together, and all the variables

2x^2-13x+16=0

a = 2; b = -13; c = +16;
Δ = b2-4ac
Δ = -132-4·2·16
Δ = 41
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{41}}{2*2}=\frac{13-\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{41}}{2*2}=\frac{13+\sqrt{41}}{4}
$