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-4x^2+24.5x=3
We move all terms to the left:
-4x^2+24.5x-(3)=0
a = -4; b = 24.5; c = -3;
Δ = b2-4ac
Δ = 24.52-4·(-4)·(-3)
Δ = 552.25
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24.5)-\sqrt{552.25}}{2*-4}=\frac{-24.5-\sqrt{552.25}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24.5)+\sqrt{552.25}}{2*-4}=\frac{-24.5+\sqrt{552.25}}{-8} $
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