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4x(2x-5)=3x+5
We move all terms to the left:
4x(2x-5)-(3x+5)=0
We multiply parentheses
8x^2-20x-(3x+5)=0
We get rid of parentheses
8x^2-20x-3x-5=0
We add all the numbers together, and all the variables
8x^2-23x-5=0
a = 8; b = -23; c = -5;
Δ = b2-4ac
Δ = -232-4·8·(-5)
Δ = 689
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{-(-23)-\sqrt{689}}{2*8}=\frac{23-\sqrt{689}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{689}}{2*8}=\frac{23+\sqrt{689}}{16} $
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