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7x(x+3)=4x-5
We move all terms to the left:
7x(x+3)-(4x-5)=0
We multiply parentheses
7x^2+21x-(4x-5)=0
We get rid of parentheses
7x^2+21x-4x+5=0
We add all the numbers together, and all the variables
7x^2+17x+5=0
a = 7; b = 17; c = +5;
Δ = b2-4ac
Δ = 172-4·7·5
Δ = 149
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{-(17)-\sqrt{149}}{2*7}=\frac{-17-\sqrt{149}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{149}}{2*7}=\frac{-17+\sqrt{149}}{14} $
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