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5x(4x+3)=22
We move all terms to the left:
5x(4x+3)-(22)=0
We multiply parentheses
20x^2+15x-22=0
a = 20; b = 15; c = -22;
Δ = b2-4ac
Δ = 152-4·20·(-22)
Δ = 1985
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{-(15)-\sqrt{1985}}{2*20}=\frac{-15-\sqrt{1985}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{1985}}{2*20}=\frac{-15+\sqrt{1985}}{40} $
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