2/5w-8=-15w+7

Solution for 2/5w-8=-15w+7 equation:

2/5w-8=-15w+7

We move all terms to the left:

2/5w-8-(-15w+7)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R


We get rid of parentheses

2/5w+15w-7-8=0

We multiply all the terms by the denominator


15w*5w-7*5w-8*5w+2=0

Wy multiply elements

75w^2-35w-40w+2=0

We add all the numbers together, and all the variables

75w^2-75w+2=0

a = 75; b = -75; c = +2;
Δ = b2-4ac
Δ = -752-4·75·2
Δ = 5025
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:

$\sqrt{\Delta}=\sqrt{5025}=\sqrt{25*201}=\sqrt{25}*\sqrt{201}=5\sqrt{201}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{201}}{2*75}=\frac{75-5\sqrt{201}}{150}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{201}}{2*75}=\frac{75+5\sqrt{201}}{150}
$