-9x(x-7)=3(x+5)

Solution for -9x(x-7)=3(x+5) equation:

-9x(x-7)=3(x+5)

We move all terms to the left:

-9x(x-7)-(3(x+5))=0

We multiply parentheses

-9x^2+63x-(3(x+5))=0


We calculate terms in parentheses: -(3(x+5)), so:

3(x+5)

We multiply parentheses

3x+15

Back to the equation:

-(3x+15)


We get rid of parentheses

-9x^2+63x-3x-15=0

We add all the numbers together, and all the variables

-9x^2+60x-15=0

a = -9; b = 60; c = -15;
Δ = b2-4ac
Δ = 602-4·(-9)·(-15)
Δ = 3060
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:

$\sqrt{\Delta}=\sqrt{3060}=\sqrt{36*85}=\sqrt{36}*\sqrt{85}=6\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-6\sqrt{85}}{2*-9}=\frac{-60-6\sqrt{85}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+6\sqrt{85}}{2*-9}=\frac{-60+6\sqrt{85}}{-18}
$