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x(5x-7)=52
We move all terms to the left:
x(5x-7)-(52)=0
We multiply parentheses
5x^2-7x-52=0
a = 5; b = -7; c = -52;
Δ = b2-4ac
Δ = -72-4·5·(-52)
Δ = 1089
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{1089}=33$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-33}{2*5}=\frac{-26}{10} =-2+3/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+33}{2*5}=\frac{40}{10} =4 $
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