5c+4=2c(c-5)

Solution for 5c+4=2c(c-5) equation:

5c+4=2c(c-5)

We move all terms to the left:

5c+4-(2c(c-5))=0


We calculate terms in parentheses: -(2c(c-5)), so:

2c(c-5)

We multiply parentheses

2c^2-10c

Back to the equation:

-(2c^2-10c)


We get rid of parentheses

-2c^2+5c+10c+4=0

We add all the numbers together, and all the variables

-2c^2+15c+4=0

a = -2; b = 15; c = +4;
Δ = b2-4ac
Δ = 152-4·(-2)·4
Δ = 257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{257}}{2*-2}=\frac{-15-\sqrt{257}}{-4}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{257}}{2*-2}=\frac{-15+\sqrt{257}}{-4}
$