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x(7x+33)=10
We move all terms to the left:
x(7x+33)-(10)=0
We multiply parentheses
7x^2+33x-10=0
a = 7; b = 33; c = -10;
Δ = b2-4ac
Δ = 332-4·7·(-10)
Δ = 1369
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{1369}=37$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-37}{2*7}=\frac{-70}{14} =-5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+37}{2*7}=\frac{4}{14} =2/7 $
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