4x2=3x+7

Solution for 4x2=3x+7 equation:

4x^2=3x+7

We move all terms to the left:

4x^2-(3x+7)=0

We get rid of parentheses

4x^2-3x-7=0

a = 4; b = -3; c = -7;
Δ = b2-4ac
Δ = -32-4·4·(-7)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-11}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+11}{2*4}=\frac{14}{8}
=1+3/4
$