15c(3c-2)=8c-2

Solution for 15c(3c-2)=8c-2 equation:

15c(3c-2)=8c-2

We move all terms to the left:

15c(3c-2)-(8c-2)=0

We multiply parentheses

45c^2-30c-(8c-2)=0

We get rid of parentheses

45c^2-30c-8c+2=0

We add all the numbers together, and all the variables

45c^2-38c+2=0

a = 45; b = -38; c = +2;
Δ = b2-4ac
Δ = -382-4·45·2
Δ = 1084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1084}=\sqrt{4*271}=\sqrt{4}*\sqrt{271}=2\sqrt{271}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{271}}{2*45}=\frac{38-2\sqrt{271}}{90}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{271}}{2*45}=\frac{38+2\sqrt{271}}{90}
$