5(2c+9)-3c(c+8)=-42

Solution for 5(2c+9)-3c(c+8)=-42 equation:

5(2c+9)-3c(c+8)=-42

We move all terms to the left:

5(2c+9)-3c(c+8)-(-42)=0

We add all the numbers together, and all the variables

5(2c+9)-3c(c+8)+42=0

We multiply parentheses

-3c^2+10c-24c+45+42=0

We add all the numbers together, and all the variables

-3c^2-14c+87=0

a = -3; b = -14; c = +87;
Δ = b2-4ac
Δ = -142-4·(-3)·87
Δ = 1240
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:

$\sqrt{\Delta}=\sqrt{1240}=\sqrt{4*310}=\sqrt{4}*\sqrt{310}=2\sqrt{310}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{310}}{2*-3}=\frac{14-2\sqrt{310}}{-6}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{310}}{2*-3}=\frac{14+2\sqrt{310}}{-6}
$