X2+7x=45-2x

Solution for X2+7x=45-2x equation:

X2+7X=45-2X

We move all terms to the left:

X2+7X-(45-2X)=0

We add all the numbers together, and all the variables

X2+7X-(-2X+45)=0

We add all the numbers together, and all the variables

X^2+7X-(-2X+45)=0

We get rid of parentheses

X^2+7X+2X-45=0

We add all the numbers together, and all the variables

X^2+9X-45=0

a = 1; b = 9; c = -45;
Δ = b2-4ac
Δ = 92-4·1·(-45)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{29}}{2*1}=\frac{-9-3\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{29}}{2*1}=\frac{-9+3\sqrt{29}}{2}
$