4a^2=-7a+6

Solution for 4a^2=-7a+6 equation:

4a^2=-7a+6

We move all terms to the left:

4a^2-(-7a+6)=0

We get rid of parentheses

4a^2+7a-6=0

a = 4; b = 7; c = -6;
Δ = b2-4ac
Δ = 72-4·4·(-6)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{145}}{2*4}=\frac{-7-\sqrt{145}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{145}}{2*4}=\frac{-7+\sqrt{145}}{8}
$