(7w-1)(6w=5)

Solution for (7w-1)(6w=5) equation:

(7w-1)(6w=5)

We move all terms to the left:

(7w-1)(6w-(5))=0

We multiply parentheses ..

(+42w^2-35w-6w+5)=0

We get rid of parentheses

42w^2-35w-6w+5=0

We add all the numbers together, and all the variables

42w^2-41w+5=0

a = 42; b = -41; c = +5;
Δ = b2-4ac
Δ = -412-4·42·5
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-29}{2*42}=\frac{12}{84}
=1/7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+29}{2*42}=\frac{70}{84}
=5/6
$