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4x(x+1)=25x+49
We move all terms to the left:
4x(x+1)-(25x+49)=0
We multiply parentheses
4x^2+4x-(25x+49)=0
We get rid of parentheses
4x^2+4x-25x-49=0
We add all the numbers together, and all the variables
4x^2-21x-49=0
a = 4; b = -21; c = -49;
Δ = b2-4ac
Δ = -212-4·4·(-49)
Δ = 1225
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1225}=35$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-35}{2*4}=\frac{-14}{8} =-1+3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+35}{2*4}=\frac{56}{8} =7 $
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