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4x^2-45x=-4
We move all terms to the left:
4x^2-45x-(-4)=0
We add all the numbers together, and all the variables
4x^2-45x+4=0
a = 4; b = -45; c = +4;
Δ = b2-4ac
Δ = -452-4·4·4
Δ = 1961
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{-(-45)-\sqrt{1961}}{2*4}=\frac{45-\sqrt{1961}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1961}}{2*4}=\frac{45+\sqrt{1961}}{8} $
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