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5x^2-34x=-24
We move all terms to the left:
5x^2-34x-(-24)=0
We add all the numbers together, and all the variables
5x^2-34x+24=0
a = 5; b = -34; c = +24;
Δ = b2-4ac
Δ = -342-4·5·24
Δ = 676
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{676}=26$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-26}{2*5}=\frac{8}{10} =4/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+26}{2*5}=\frac{60}{10} =6 $
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