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6x(3x+7)=5x-13
We move all terms to the left:
6x(3x+7)-(5x-13)=0
We multiply parentheses
18x^2+42x-(5x-13)=0
We get rid of parentheses
18x^2+42x-5x+13=0
We add all the numbers together, and all the variables
18x^2+37x+13=0
a = 18; b = 37; c = +13;
Δ = b2-4ac
Δ = 372-4·18·13
Δ = 433
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{-(37)-\sqrt{433}}{2*18}=\frac{-37-\sqrt{433}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{433}}{2*18}=\frac{-37+\sqrt{433}}{36} $
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