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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

3x+(-2x+7)x-9=0

We multiply parentheses

-2x^2+3x+7x-9=0

We add all the numbers together, and all the variables

-2x^2+10x-9=0

a = -2; b = 10; c = -9;
Δ = b2-4ac
Δ = 102-4·(-2)·(-9)
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{7}}{2*-2}=\frac{-10-2\sqrt{7}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{7}}{2*-2}=\frac{-10+2\sqrt{7}}{-4}
$