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4x(3x-5)=5x+35
We move all terms to the left:
4x(3x-5)-(5x+35)=0
We multiply parentheses
12x^2-20x-(5x+35)=0
We get rid of parentheses
12x^2-20x-5x-35=0
We add all the numbers together, and all the variables
12x^2-25x-35=0
a = 12; b = -25; c = -35;
Δ = b2-4ac
Δ = -252-4·12·(-35)
Δ = 2305
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{-(-25)-\sqrt{2305}}{2*12}=\frac{25-\sqrt{2305}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{2305}}{2*12}=\frac{25+\sqrt{2305}}{24} $
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