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X(12X+3)=1141
We move all terms to the left:
X(12X+3)-(1141)=0
We multiply parentheses
12X^2+3X-1141=0
a = 12; b = 3; c = -1141;
Δ = b2-4ac
Δ = 32-4·12·(-1141)
Δ = 54777
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{54777}=\sqrt{961*57}=\sqrt{961}*\sqrt{57}=31\sqrt{57}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-31\sqrt{57}}{2*12}=\frac{-3-31\sqrt{57}}{24} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+31\sqrt{57}}{2*12}=\frac{-3+31\sqrt{57}}{24} $
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