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(10x+5)(-3x+12)=7
We move all terms to the left:
(10x+5)(-3x+12)-(7)=0
We multiply parentheses ..
(-30x^2+120x-15x+60)-7=0
We get rid of parentheses
-30x^2+120x-15x+60-7=0
We add all the numbers together, and all the variables
-30x^2+105x+53=0
a = -30; b = 105; c = +53;
Δ = b2-4ac
Δ = 1052-4·(-30)·53
Δ = 17385
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{-(105)-\sqrt{17385}}{2*-30}=\frac{-105-\sqrt{17385}}{-60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{17385}}{2*-30}=\frac{-105+\sqrt{17385}}{-60} $
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