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

Solution for 7+3x=2(x-9)x= equation:

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

We move all terms to the left:

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


We calculate terms in parentheses: -(2(x-9)x), so:

2(x-9)x

We multiply parentheses

2x^2-18x

Back to the equation:

-(2x^2-18x)


We get rid of parentheses

-2x^2+3x+18x+7=0

We add all the numbers together, and all the variables

-2x^2+21x+7=0

a = -2; b = 21; c = +7;
Δ = b2-4ac
Δ = 212-4·(-2)·7
Δ = 497
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{-(21)-\sqrt{497}}{2*-2}=\frac{-21-\sqrt{497}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{497}}{2*-2}=\frac{-21+\sqrt{497}}{-4}
$