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(3x+2.5)(4x+3.25)=26.25
We move all terms to the left:
(3x+2.5)(4x+3.25)-(26.25)=0
We add all the numbers together, and all the variables
(3x+2.5)(4x+3.25)-26.25=0
We multiply parentheses ..
(+12x^2+9.75x+10x+8.125)-26.25=0
We get rid of parentheses
12x^2+9.75x+10x+8.125-26.25=0
We add all the numbers together, and all the variables
12x^2+19.75x-18.125=0
a = 12; b = 19.75; c = -18.125;
Δ = b2-4ac
Δ = 19.752-4·12·(-18.125)
Δ = 1260.0625
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{-(19.75)-\sqrt{1260.0625}}{2*12}=\frac{-19.75-\sqrt{1260.0625}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19.75)+\sqrt{1260.0625}}{2*12}=\frac{-19.75+\sqrt{1260.0625}}{24} $
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