2.5(x)=2x^2+3x-7

Solution for 2.5(x)=2x^2+3x-7 equation:

2.5(x)=2x^2+3x-7

We move all terms to the left:

2.5(x)-(2x^2+3x-7)=0

We get rid of parentheses

-2x^2+2.5x-3x+7=0

We add all the numbers together, and all the variables

-2x^2-0.5x+7=0

a = -2; b = -0.5; c = +7;
Δ = b2-4ac
Δ = -0.52-4·(-2)·7
Δ = 56.25
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{-(-0.5)-\sqrt{56.25}}{2*-2}=\frac{0.5-\sqrt{56.25}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{56.25}}{2*-2}=\frac{0.5+\sqrt{56.25}}{-4}
$