.(4w+3)/3=5w-7

Solution for .(4w+3)/3=5w-7 equation:

.(4w+3)/3=5w-7

We move all terms to the left:

.(4w+3)/3-(5w-7)=0

We get rid of parentheses

.(4w+3)/3-5w+7=0

We multiply all the terms by the denominator


.(4w+3)-5w*3+7*3=0

We add all the numbers together, and all the variables

.(4w+3)-5w*3+21=0

We multiply parentheses

4w^2-5w*3+21+=0

Wy multiply elements

4w^2-15w+21+=0

We add all the numbers together, and all the variables

4w^2-15w=0

a = 4; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·4·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*4}=\frac{0}{8}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*4}=\frac{30}{8}
=3+3/4
$