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4x^2-29x+45=-5+10
We move all terms to the left:
4x^2-29x+45-(-5+10)=0
We add all the numbers together, and all the variables
4x^2-29x+45-5=0
We add all the numbers together, and all the variables
4x^2-29x+40=0
a = 4; b = -29; c = +40;
Δ = b2-4ac
Δ = -292-4·4·40
Δ = 201
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{-(-29)-\sqrt{201}}{2*4}=\frac{29-\sqrt{201}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{201}}{2*4}=\frac{29+\sqrt{201}}{8} $
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