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48-(2c+3)=4(c+6)c
We move all terms to the left:
48-(2c+3)-(4(c+6)c)=0
We get rid of parentheses
-2c-(4(c+6)c)-3+48=0
We calculate terms in parentheses: -(4(c+6)c), so:We add all the numbers together, and all the variables
4(c+6)c
We multiply parentheses
4c^2+24c
Back to the equation:
-(4c^2+24c)
-2c-(4c^2+24c)+45=0
We get rid of parentheses
-4c^2-2c-24c+45=0
We add all the numbers together, and all the variables
-4c^2-26c+45=0
a = -4; b = -26; c = +45;
Δ = b2-4ac
Δ = -262-4·(-4)·45
Δ = 1396
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}$$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1396}=\sqrt{4*349}=\sqrt{4}*\sqrt{349}=2\sqrt{349}$$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{349}}{2*-4}=\frac{26-2\sqrt{349}}{-8} $$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{349}}{2*-4}=\frac{26+2\sqrt{349}}{-8} $
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