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x(2x+7)=52
We move all terms to the left:
x(2x+7)-(52)=0
We multiply parentheses
2x^2+7x-52=0
a = 2; b = 7; c = -52;
Δ = b2-4ac
Δ = 72-4·2·(-52)
Δ = 465
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{-(7)-\sqrt{465}}{2*2}=\frac{-7-\sqrt{465}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{465}}{2*2}=\frac{-7+\sqrt{465}}{4} $
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