-3/4w=3w+10

Solution for -3/4w=3w+10 equation:

-3/4w=3w+10

We move all terms to the left:

-3/4w-(3w+10)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We get rid of parentheses

-3/4w-3w-10=0

We multiply all the terms by the denominator


-3w*4w-10*4w-3=0

Wy multiply elements

-12w^2-40w-3=0

a = -12; b = -40; c = -3;
Δ = b2-4ac
Δ = -402-4·(-12)·(-3)
Δ = 1456
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:

$\sqrt{\Delta}=\sqrt{1456}=\sqrt{16*91}=\sqrt{16}*\sqrt{91}=4\sqrt{91}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{91}}{2*-12}=\frac{40-4\sqrt{91}}{-24}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{91}}{2*-12}=\frac{40+4\sqrt{91}}{-24}
$