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5w^2=11w+12
We move all terms to the left:
5w^2-(11w+12)=0
We get rid of parentheses
5w^2-11w-12=0
a = 5; b = -11; c = -12;
Δ = b2-4ac
Δ = -112-4·5·(-12)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{361}=19$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-19}{2*5}=\frac{-8}{10} =-4/5 $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+19}{2*5}=\frac{30}{10} =3 $
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