4x^2+7x=7.5

Solution for 4x^2+7x=7.5 equation:

4x^2+7x=7.5

We move all terms to the left:

4x^2+7x-(7.5)=0

We add all the numbers together, and all the variables

4x^2+7x-7.5=0

a = 4; b = 7; c = -7.5;
Δ = b2-4ac
Δ = 72-4·4·(-7.5)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*4}=\frac{-20}{8}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*4}=\frac{6}{8}
=3/4
$