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4x=(x+30)(5x-25)
We move all terms to the left:
4x-((x+30)(5x-25))=0
We multiply parentheses ..
-((+5x^2-25x+150x-750))+4x=0
We calculate terms in parentheses: -((+5x^2-25x+150x-750)), so:We add all the numbers together, and all the variables
(+5x^2-25x+150x-750)
We get rid of parentheses
5x^2-25x+150x-750
We add all the numbers together, and all the variables
5x^2+125x-750
Back to the equation:
-(5x^2+125x-750)
4x-(5x^2+125x-750)=0
We get rid of parentheses
-5x^2+4x-125x+750=0
We add all the numbers together, and all the variables
-5x^2-121x+750=0
a = -5; b = -121; c = +750;
Δ = b2-4ac
Δ = -1212-4·(-5)·750
Δ = 29641
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{-(-121)-\sqrt{29641}}{2*-5}=\frac{121-\sqrt{29641}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-121)+\sqrt{29641}}{2*-5}=\frac{121+\sqrt{29641}}{-10} $
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