-9+7=2(5-x);x=4

Solution for -9+7=2(5-x);x=4 equation:

-9+7=2(5-x)x=4

We move all terms to the left:

-9+7-(2(5-x)x)=0

We add all the numbers together, and all the variables

-(2(-1x+5)x)-9+7=0

We add all the numbers together, and all the variables

-(2(-1x+5)x)-2=0


We calculate terms in parentheses: -(2(-1x+5)x), so:

2(-1x+5)x

We multiply parentheses

-2x^2+10x

Back to the equation:

-(-2x^2+10x)


We get rid of parentheses

2x^2-10x-2=0

a = 2; b = -10; c = -2;
Δ = b2-4ac
Δ = -102-4·2·(-2)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{29}}{2*2}=\frac{10-2\sqrt{29}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{29}}{2*2}=\frac{10+2\sqrt{29}}{4}
$