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4x+(15x+3)7x-5=180
We move all terms to the left:
4x+(15x+3)7x-5-(180)=0
We add all the numbers together, and all the variables
4x+(15x+3)7x-185=0
We multiply parentheses
105x^2+4x+21x-185=0
We add all the numbers together, and all the variables
105x^2+25x-185=0
a = 105; b = 25; c = -185;
Δ = b2-4ac
Δ = 252-4·105·(-185)
Δ = 78325
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{78325}=\sqrt{25*3133}=\sqrt{25}*\sqrt{3133}=5\sqrt{3133}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{3133}}{2*105}=\frac{-25-5\sqrt{3133}}{210} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{3133}}{2*105}=\frac{-25+5\sqrt{3133}}{210} $
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