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10x^2=9x+7
We move all terms to the left:
10x^2-(9x+7)=0
We get rid of parentheses
10x^2-9x-7=0
a = 10; b = -9; c = -7;
Δ = b2-4ac
Δ = -92-4·10·(-7)
Δ = 361
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{361}=19$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-19}{2*10}=\frac{-10}{20} =-1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+19}{2*10}=\frac{28}{20} =1+2/5 $
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