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2x(2x+1)-7(x+1)=0
We multiply parentheses
4x^2+2x-7x-7=0
We add all the numbers together, and all the variables
4x^2-5x-7=0
a = 4; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·4·(-7)
Δ = 137
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{-(-5)-\sqrt{137}}{2*4}=\frac{5-\sqrt{137}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{137}}{2*4}=\frac{5+\sqrt{137}}{8} $
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