9x2+54x=79(x2+6x)=79(x2+6x+9)=7+

Solution for 9x2+54x=79(x2+6x)=79(x2+6x+9)=7+ equation:

9x^2+54x=79(x2+6x)=79(x2+6x+9)=7+

We move all terms to the left:

9x^2+54x-(79(x2+6x))=0

We add all the numbers together, and all the variables

9x^2-(79(+x^2+6x))+54x=0


We calculate terms in parentheses: -(79(+x^2+6x)), so:

79(+x^2+6x)

We multiply parentheses

79x^2+474x

Back to the equation:

-(79x^2+474x)


We add all the numbers together, and all the variables

9x^2+54x-(79x^2+474x)=0

We get rid of parentheses

9x^2-79x^2+54x-474x=0

We add all the numbers together, and all the variables

-70x^2-420x=0

a = -70; b = -420; c = 0;
Δ = b2-4ac
Δ = -4202-4·(-70)·0
Δ = 176400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{176400}=420$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-420}{2*-70}=\frac{0}{-140}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+420}{2*-70}=\frac{840}{-140}
=-6
$