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4x^2=-13x+3
We move all terms to the left:
4x^2-(-13x+3)=0
We get rid of parentheses
4x^2+13x-3=0
a = 4; b = 13; c = -3;
Δ = b2-4ac
Δ = 132-4·4·(-3)
Δ = 217
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{-(13)-\sqrt{217}}{2*4}=\frac{-13-\sqrt{217}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{217}}{2*4}=\frac{-13+\sqrt{217}}{8} $
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