2(3c)2-5(3c)=7

Solution for 2(3c)2-5(3c)=7 equation:

2(3c)2-5(3c)=7

We move all terms to the left:

2(3c)2-5(3c)-(7)=0

We add all the numbers together, and all the variables

23c^2-53c-7=0

a = 23; b = -53; c = -7;
Δ = b2-4ac
Δ = -532-4·23·(-7)
Δ = 3453
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{-(-53)-\sqrt{3453}}{2*23}=\frac{53-\sqrt{3453}}{46}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{3453}}{2*23}=\frac{53+\sqrt{3453}}{46}
$