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4x^2-7x=13
We move all terms to the left:
4x^2-7x-(13)=0
a = 4; b = -7; c = -13;
Δ = b2-4ac
Δ = -72-4·4·(-13)
Δ = 257
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{-(-7)-\sqrt{257}}{2*4}=\frac{7-\sqrt{257}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{257}}{2*4}=\frac{7+\sqrt{257}}{8} $
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