-9w(-5w-7)+7w=-6w+179

Solution for -9w(-5w-7)+7w=-6w+179 equation:

-9w(-5w-7)+7w=-6w+179

We move all terms to the left:

-9w(-5w-7)+7w-(-6w+179)=0

We add all the numbers together, and all the variables

7w-9w(-5w-7)-(-6w+179)=0

We multiply parentheses

45w^2+7w+63w-(-6w+179)=0

We get rid of parentheses

45w^2+7w+63w+6w-179=0

We add all the numbers together, and all the variables

45w^2+76w-179=0

a = 45; b = 76; c = -179;
Δ = b2-4ac
Δ = 762-4·45·(-179)
Δ = 37996
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{37996}=\sqrt{4*9499}=\sqrt{4}*\sqrt{9499}=2\sqrt{9499}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-2\sqrt{9499}}{2*45}=\frac{-76-2\sqrt{9499}}{90}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+2\sqrt{9499}}{2*45}=\frac{-76+2\sqrt{9499}}{90}
$